School of Arts and Sciences

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

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.

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.

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

Social Activities

 1