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Yoshiyuki Ohyama

  (大山 淑之)

Profile Information

Affiliation
Professor, School of Arts and Sciences, Tokyo Woman's Christian University
Degree
Docter of Science(Mar, 1992, Waseda University)
理学修士(Mar, 1987, 早稲田大学)
J-GLOBAL ID
200901010817271379
researchmap Member ID
1000162536

Research Interests

 2

Research Areas

 1

Education

 4

Papers

 11
  • Yoshiyuki Ohyama, Migiwa Sakurai
    Tokyo Journal of Mathematics, 46(1) 19-31, Jun, 2023  Peer-reviewedLead author
  • Yoshiyuki OHYAMA, Migiwa SAKURAI
    Journal of the Mathematical Society of Japan, 73(3), Jul 27, 2021  Peer-reviewedLead author
  • Yoshiyuki Ohyama, Migiwa Sakurai
    Journal of Knot Theory and Its Ramifications, 28(12) 1950074-1950074, Oct, 2019  Peer-reviewedLead author
    Satoh and Taniguchi introduced the [Formula: see text]-writhe [Formula: see text] for each non-zero integer [Formula: see text], which is an invariant for virtual knots. The [Formula: see text]-writhes give the coefficients of some polynomial invariants for virtual knots including the index polynomial, the odd writhe polynomial and the affine index polynomial. It is obvious that the virtualization of a real crossing is an unknotting operation for virtual knots. The values of [Formula: see text]-writhes changed by some local moves are calculated. However for the virtualization, it is unknown. In this paper, we show that for any given non-zero integer [Formula: see text] and any given integer [Formula: see text], there exists a virtual knot whose unknotting number by the virtualization is one and the value of the [Formula: see text]-writhe equals [Formula: see text]. Namely, the virtualization of a real crossing changes the value of [Formula: see text]-writhe by any given integer [Formula: see text].
  • Sumiko Horiuchi, Yoshiyuki Ohyama
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 26(13), Nov, 2017  Peer-reviewed
    We consider a local move, denoted by., on knot diagrams or virtual knot diagrams. If two (virtual) knots K-1 and K-2 are transformed into each other by a finite sequence of lambda moves, the lambda distance between K-1 and K-2 is the minimum number of times of lambda moves needed to transform K-1 into K-2. By Gamma(lambda)(K), we denote the set of all (virtual) knots which can be transformed into a (virtual) knot K by lambda moves. A geodesic graph for Gamma(lambda)(K) is the graph which satisfies the following: The vertex set consists of (virtual) knots in Gamma(lambda)(K) and for any two vertices K-1 and K-2, the distance on the graph from K-1 to K-2 coincides with the lambda distance between K-1 and K-2. When we consider virtual knots and a crossing change as a local move lambda, we show that the N-dimensional lattice graph for any given natural number N and any tree are geodesic graphs for Gamma(lambda)(K).
  • Sumiko Horiuchi, Yoshiyuki Ohyama
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 23(4), Apr, 2014  Peer-reviewed
    A local move called a C-n-move is closely related to Vassiliev invariants. The C-n-distance between two knots K and L, denoted by d(Cn) (K, L), is the minimal number of C-n-moves needed to transform K into L. In the case of n >= 3, we show that for any pair of knots K-1 and K-2 with d(Cn) (K-1, K-2) = 1 and for any given natural number m, there exist infinitely many knots J(j) (j = 1, 2,...) such that dC(n) (K1, J(j)) = d(Cn) (J(j), K-2) = 1 and they have the same Vassiliev invariants of order less than or equal to m.
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Misc.

 54
  • Sumiko Horiuchi, Yoshiyuki Ohyama
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 19(4) 503-507, Apr, 2010  
    Adams et al. introduce the notion of almost alternating links; non-alternating links which have a projection whose one crossing change yields an alternating projection. For an alternating knot K, we consider the number Alm(K) of almost alternating knots which have a projection whose one crossing change yields K. We show that for any given natural number n, there is an alternating knot K with Alm(K) >= n.
  • Sumiko Horiuchi, Yoshiyuki Ohyama
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 19(4) 503-507, Apr, 2010  
    Adams et al. introduce the notion of almost alternating links; non-alternating links which have a projection whose one crossing change yields an alternating projection. For an alternating knot K, we consider the number Alm(K) of almost alternating knots which have a projection whose one crossing change yields K. We show that for any given natural number n, there is an alternating knot K with Alm(K) >= n.
  • Yasutaka Nakanishi, Yoshiyuki Ohyama
    HIROSHIMA MATHEMATICAL JOURNAL, 39(3) 443-450, Nov, 2009  
    After the works of Kauffman-Banchoff and Yamasaki, it is known that a local move called the pass move is strongly related to the Arf invariant, which is equivalent to the parity of the coefficient of the degree two term in the Conway polynomial. Our main result is the following: There exists a pair of knots such that their Conway polynomials coincide, and that the sets of Conway polynomials of knots obtained from them by a single pass move do not coincide.
  • Yasutaka Nakanishi, Yoshiyuki Ohyama
    Hiroshima Mathematical Journal, 39(3) 443-450, 2009  
  • Yoshiyuki Ohyama, Harumi Yamada
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 17(7) 771-785, Jul, 2008  
    It is shown that two knots can be transformed into each other by C-n-moves if and only if they have the same Vassiliev invariants of order less than n. Consequently, a C-n-move cannot change the Vassiliev invariants of order less than n and may change those of order more than or equal to n. In this paper, we consider the coefficient of the Conway polynomial as a Vassiliev invariant and show that a Cn-move changes the nth coefficient of the Conway polynomial by +/- 2, or 0. And for the 2mth coefficient (2m > n), it can change by p or p + 1 for any given integer p.
  • Yoshiyuki Ohyama, Harumi Yamada
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 17(7) 771-785, Jul, 2008  
    It is shown that two knots can be transformed into each other by C-n-moves if and only if they have the same Vassiliev invariants of order less than n. Consequently, a C-n-move cannot change the Vassiliev invariants of order less than n and may change those of order more than or equal to n. In this paper, we consider the coefficient of the Conway polynomial as a Vassiliev invariant and show that a Cn-move changes the nth coefficient of the Conway polynomial by +/- 2, or 0. And for the 2mth coefficient (2m > n), it can change by p or p + 1 for any given integer p.
  • Yasutaka Nakanishi, Yoshiyuki Ohyama
    Journal of Knot Theory and its Ramifications, 15(9) 1215-1224, Nov, 2006  
    By the works of Gusarov [2] and Habiro [3], it is known that a local move called the Cn move is strongly related to Vassiliev invariants of order less than n. The coefficient of the zn term in the Conway polynomial is known to be a Vassiliev invariant of order n. In this note, we will consider to what degree the relationship is strong with respect to Conway polynomial. Let K be a knot, and KCn the set of knots obtained from a knot K by a single Cn move. Let ∇K be the set of the Conway polynomials {∇K(z)}K∈K, for a set of knots K. Our main result is the following: There exists a pair of knots K1, K2 such that ∇K1 = ∇K2, and ∇K1 Cn ≠ ∇K2 Cn. In other words, the Cn Gordian complex is not homogeneous with respect to Conway polynomial. © World Scientific Publishing Company.
  • Yasutaka Nakanishi, Yoshiyuki Ohyama
    Journal of Knot Theory and its Ramifications, 15(9) 1215-1224, Nov, 2006  
    By the works of Gusarov [2] and Habiro [3], it is known that a local move called the Cn move is strongly related to Vassiliev invariants of order less than n. The coefficient of the zn term in the Conway polynomial is known to be a Vassiliev invariant of order n. In this note, we will consider to what degree the relationship is strong with respect to Conway polynomial. Let K be a knot, and KCn the set of knots obtained from a knot K by a single Cn move. Let ∇K be the set of the Conway polynomials {∇K(z)}K∈K, for a set of knots K. Our main result is the following: There exists a pair of knots K1, K2 such that ∇K1 = ∇K2, and ∇K1 Cn ≠ ∇K2 Cn. In other words, the Cn Gordian complex is not homogeneous with respect to Conway polynomial. © World Scientific Publishing Company.
  • Y Nakanishi, Y Ohyama
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 15(2) 205-215, Feb, 2006  
    It is well-known that the coefficient of z(m) of the Conway polynomial is a Vassiiev invariant of order m. In this paper, we show that for any given pair of a natural number n and a knot K, there exist infinitely many knots whose Vassiliev invariants of order less than or equal to n and Conway polynomials coincide with those of K.
  • Yasutaka Nakanishi, Yoshiyuki Ohyama
    Journal of Knot Theory and its Ramifications, 15(2) 205-215, Feb, 2006  
    It is well-known that the coefficient of zm of the Conway polynomial is a Vassiiev invariant of order m. In this paper, we show that for any given pair of a natural number n and a knot K, there exist infinitely many knots whose Vassiliev invariants of order less than or equal to n and Conway polynomials coincide with those of K. © World Scientific Publishing Company.
  • Y Ohyama
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 15(1) 73-80, Jan, 2006  
    Hirasawa, and Uchida defined the Gordian complex of knots which is a simplicial complex whose vertices consist of all knot types in S-3 by using "a crossing change". In this paper, we define the C-k-Gordian complex of knots which is an extension of the Gordian complex of knots. Let k be a natural number more than 2 and we show that for any knot K-0 and any given natural number n, there exists a family of knots {K-0, K-1,..., K-n} such that for any pair (K-i, K-j) of distinct elements of the family, the C-k-distance d(Ck) (K-i, K-j) = 1.
  • Yoshiyuki Ohyama
    Journal of Knot Theory and its Ramifications, 15(1) 73-80, Jan, 2006  
    Hirasawa and Uchida defined the Gordian complex of knots which is a simplicial complex whose vertices consist of all knot types in S3 by using "a crossing change". In this paper, we define the C ke-Gordian complex of knots which is an extension of the Gordian complex of knots. Let k be a natural number more than 2 and we show that for any knot K0 and any given natural number n, there exists a family of knots {K0, K1 ,..., Kn} such that for any pair (Ki, Kj) of distinct elements of the family, the C k-distance dCk,(Ki, Kj) = 1. © World Scientific Publishing Company.
  • Y Nakanishi, Y Ohyama
    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 55(3) 641-654, Jul, 2003  
    In this note, we will study Delta link homotopy, which is an equivalence relation of ordered and oriented link types. Previously, a necessary condition was given by a pair of numerical invariants derived from the Conway polynomials for two link types to be Delta link homotopic. In this note, we will show that, for two component links, if their pairs of numerical invariants coincide then the two links are Delta link homotopic.
  • Yasutaka Nakanishi, Yoshiyuki Ohyama
    Journal of the Mathematical Society of Japan, 55(3) 641-654, 2003  
    In this note, we will study Delta link homotopy, which is an equivalence relation of ordered and oriented link types. Previously, a necessary condition was given by a pair of numerical invariants derived from the Conway polynomials for two link types to be Delta link homotopic. In this note, we will show that, for two component links, if their pairs of numerical invariants coincide then the two links are Delta link homotopic. © 2003 Applied Probability Trust.
  • Y Ohyama
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 11(4) 507-514, Jun, 2002  
    By the same way for knots, it can be proved that if a link L is transformed into L' by a C-n-move, the difference of the Vassiliev invariants of order n between L and L' is equal to the value of the one-branch tree diagram corresponding to the C-n-move. In this paper we show that a C-n-move for a link whose one-branch tree diagram has a cut edge cannot change the Vassiliev invariant of order n. And from this, we can give some examples of links that have the same Vassiliev invariants of order less than n and cannot be transformed into each other by C-n-moves.
  • Y Ohyama, H Yamada
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 11(4) 515-526, Jun, 2002  
    In this paper, we show that when any nonnegative integer n and any knot K are given, there exist infinitely many unknotting number one knots J(m) (m = 1, 2,(. . .)) such that their Vassiliev invariants of order less than or equal to n coincide with those of K and each J(m) satisfies the following: The delta unknotting number of J(m) is determined by the order two Vassiliev invariant of K and for almost cases, the clasp-pass distance between J(m) and the twist knot with the same order two invariant is determined by the order three invariant of K.
  • Y Nakanishi, Y Ohyama
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 11(3) 353-362, May, 2002  
    In this note, we will study A link homotopy (or self Delta-equivalence), which is an equivalence relation of ordered and oriented link types. Previously, a necessary condition is given in the terms of Conway polynomials for two link types to be Delta link homotopic. A pair of numerical invariants delta(1) and delta(2) classifies all (ordered and oriented) prime 2-component link types with seven crossings or less up to Delta link homotopy. We will show here that for any pair of integers n(1) and n(2) there exists a 2-component link K such that delta(1) (K) = n(1) and delta(2) (K) = n(2) provided that at least one of n(1) and n(2) is even.
  • OHYAMA Y.
    Tokyo J. Math., 25(1) 17-31, 2002  
  • Yoshiyuki Ohyama
    Journal of Knot Theory and its Ramifications, 11(4) 507-514, 2002  
    By the same way for knots, it can be proved that if a link L is transformed into L′ by a Cn-move, the difference of the Vassiliev invariants of order n between L and L′ is equal to the value of the one-branch tree diagram corresponding to the Cn-move. In this paper we show that a Cn-move for a link whose one-branch tree diagram has a cut edge cannot change the Vassiliev invariant of order n. And from this, we can give some examples of links that have the same Vassiliev invariants of order less than n and cannot be transformed into each other by Cn-moves.
  • Yoshiyuki Ohyama, Harumi Yamada
    Journal of Knot Theory and its Ramifications, 11(4) 515-526, 2002  
    In this paper, we show that when any nonnegative integer n and any knot K are given, there exist infinitely many unknotting number one knots Jm (m = 1, 2, ⋯) such that their Vassiliev invariants of order less than or equal to n coincide with those of K and each Jm satisfies the following: The delta unknotting number of Jm is determined by the order two Vassiliev invariant of K and for almost cases, the clasp-pass distance between Jm and the twist knot with the same order two invariant is determined by the order three invariant of K.
  • Tokyo Journal of Mathematics, 25(1) 17-31, 2002  
  • Yasutaka Nakanishi, Yoshiyuki Ohyama
    Journal of Knot Theory and its Ramifications, 11(3) 353-362, 2002  
    In this note, we will study Δ link homotopy (or self Δ-equivalence), which is an equivalence relation of ordered and oriented link types. Previously, a necessary condition is given in the terms of Conway polynomials for two link types to be Δ link homotopic. A pair of numerical invariants δ1 and δ2 classifies all (ordered and oriented) prime 2-component link types with seven crossings or less up to Δ link homotopy. We will show here that for any pair of integers n1 and n2 there exists a 2-component link κ such that δ1(κ) = n1 and δ2(κ) = n2 provided that at least one of n1 and n2 is even.
  • Y Nakanishi, Y Ohyama
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 10(7) 1041-1046, Nov, 2001  
    We show that for any given pair of a natural number n and a knot K, there are infinitely many knots J(m) (m = 1,2....) such that their Vassiliev invariants of order less than or equal to n coincide with those of K and that each J(m) has C-k-distance 1 (k not equal 2, k = 1,...,n) and C-2-distance 2 from the knot K. The C-k-distance means the minimum number of C-k-moves which transform one knot into the other.
  • Yasutaka Nakanishi, Yoshiyuki Ohyama
    Journal of Knot Theory and its Ramifications, 10(7) 1041-1046, Nov, 2001  
    We show that for any given pair of a natural number n and a knot Κ, there are infinitely many knots Jm (m = 1, 2, . . .) such that their Vassiliev invariants of order less than or equal to n coincide with those of K and that each Jm has Ck-distance 1 (k ≠ 2, k = 1, . . . , n) and C2-distance 2 from the knot Κ. The Ck-distance means the minimum number of Ck-moves which transform one knot into the other.
  • Y Ohyama, K Taniyama
    PACIFIC JOURNAL OF MATHEMATICS, 200(1) 191-205, Sep, 2001  
    We show that the Vassiliev invariants of the knots contained in an embedding of a graph G into R-3 satisify certain equations that are independent of the choice of the embedding of G. By a similar observation we de ne certain edge-homotopy invariants and vertex-homotopy invariants of spatial graphs based on the Vassiliev invariants of the knots contained in a spatial graph. A graph G is called adaptable if, given a knot type for each cycle of G, there is an embedding of G into R-3 that realizes all of these knot types. As an application we show that a certain planar graph is not adaptable.
  • Pacific Journal of Mathematics, 200(1) 191-205, 2001  
  • Y Ohyama
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 9(5) 693-701, Aug, 2000  
    Recently it has been proved by K. Taniyama, S. Yamada and the author that for any natural number n and any knot K, there are infinitely many unknotting number one knots, ail of whose Vassiliev invariants of order less than or equal to n coincide with those of K. In this paper we give another proof of this result by using web diagrams.
  • Journal of Knot Theory and its Ramifcations, 9(5) 693-701, 2000  
  • Y Ohyama, T Tsukamoto
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 8(1) 15-26, Feb, 1999  
    Recently it has been proved by Habiro that two knots K-1 and K-2 have the same Vassiliev invariants of order less than or equal to n if and only if K-1 and K-2 can be transformed into each other by a finite sequence of Cn+1 -moves. In this paper, we show that the difference of the Vassiliev invariants of order n between two knots that can be transformed into each other by a C-n-move is equal to the value of the Vassiliev invariant for a one-branch tree diagram of order n.
  • Yoshiyuki Ohyama, Tatsuya Tsukamoto
    Journal of Knot Theory and its Ramifications, 8(1) 15-26, 1999  
    Recently it has been proved by Habiro that two knots K1 and K2 have the same Vassiliev invariants of order less than or equal to n if and only if K1 and K2 can be transformed into each other by a finite sequence of Cn+1-moves. In this paper, we show that the difference of the Vassiliev invariants of order n between two knots that can be transformed into each other by a Cn-move is equal to the value of the Vassiliev invariant for a one-branch tree diagram of order n.
  • Y Ohyama
    TOPOLOGY AND ITS APPLICATIONS, 75(3) 201-215, Feb, 1997  
    In this paper, we restrict the Vassiliev invariants of order at most n to a twist sequence. And we study the dimension of the space of them and the topological information that the Vassiliev invariants give on a twist sequence.
  • Proceedings of Applied Mathematics Workshop (KAIST), 8, 219-225, 1997  
  • Proceedings of Applied Mathematics Workshop(KAIST), (8) 219-225, 1997  
  • Topology and its Applications, 75 201-215, 1997  
  • Y Ohyama
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 5(2) 265-277, Apr, 1996  
    We extend a notion, an unknotting operation for knots, to a spatial embedding of a graph and study local moves on a diagram of a spatial graph.
  • Journal of Knot Theory and its Ramifications, 15(2) 265-277, 1996  
  • Journal of Combinatorial Mathematics and Combinatorial Computings, 18, 3-10, 1995  
  • Y OHYAMA
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 123(1) 287-291, Jan, 1995  
    We show that for any knot K and any natural number n, we can construct infinitely many knots, all of whose finite type invariants of order at most n coincide with those of K.
  • Journal of Combinatorial Mathematics and Combinatorial Computing, (18) 3-10, 1995  
  • Yoshiyuki Ohyama
    Proceedings of the American Mathematical Society, 123(1) 287-291, 1995  
    We show that for any knot K and any natural number n, we can construct infinitely many knots, all of whose finite type invariants of order at most n coincide with those of K. © 1995 American Mathematical Society.
  • Revista Matematica de la Universidad Complutense de Madrid, 7(2) 289-305, 1994  
  • Revista Matematica de la Universidad Complutense de Madrid, 7(2) 247-277, 1994  
  • Revista Matematica de la Universidad Complutense de Madrid, 7(2) 289-305, 1994  
  • Revista Matematica de la Universidad Complutense de Madrid, 7(2) 247-277, 1994  
  • Y OHYAMA
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 45(1) 117-131, Feb, 1993  
    In this paper we prove an inequality that involves the minimal crossing number and the braid index of links by estimating Murasugi and Przytycki's index for a planar bipartite graph.
  • Canadian Journal of Mathematics, 45(1) 117-131, 1993  
  • Tokyo Journal of Mathematics, 15(2) 357-363, 1992  
  • Yoshiyuki Ohyama
    Tokyo Journal of Mathematics, 15(2) 357-363, 1992  
  • Y OHYAMA
    TOPOLOGY AND ITS APPLICATIONS, 37(3) 249-255, Dec, 1990  
    In this paper, we define a new numerical invariant of knots induced from their regular diagrams, and connect it with the Conway polynomials.
  • Yoshiyuki Ohyama, Yasuko Ogushi
    Tokyo Journal of Mathematics, 13(1) 179-190, 1990  

Books and Other Publications

 2

Presentations

 1

Professional Memberships

 2

Research Projects

 39
  • Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Apr, 2021 - Mar, 2025
  • 科学研究費助成事業, 日本学術振興会, Apr, 2016 - Mar, 2021
    大槻 知忠, 金信 泰造, 伊藤 哲也, 谷山 公規, 藤原 耕二, 逆井 卓也, 大山 淑之, 山下 靖, 茂手木 公彦, 森藤 孝之, 玉木 大, 志摩 亜希子
  • Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Apr, 2015 - Mar, 2020
    Sakuma Makoto
  • Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Apr, 2012 - Mar, 2017
    Ohtsuki Tomotada, KAMADA Seiichi, HABIRO Kazuo
  • Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Apr, 2012 - Mar, 2017
    KAWAUCHI Akio, KAMADA Seiichi, SAKUMA Makoto, NAKANISHI Yasutaka, TANIYAMA Kouki, OOYAMA Toshiyuki, MOTEGI Kimihiko, GOUDA Hiroshi, SHIMOKAWA Koya, TERAGAITO Masakazu, SATOU Shin, TANAKA Toshihumi, IWAKIRI Masahide, CHON Inde, KISHIMOTO Kengo, OTSUKI Tomotada, SHIMIZU Ayaka
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Social Activities

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