Division of Mathematical Sciences

大山 淑之

オオヤマ ヨシユキ  (Yoshiyuki Ohyama)

基本情報

所属
東京女子大学 現代教養学部 数理科学科 数学専攻 教授
学位
博士(理学)(1992年3月 早稲田大学)
理学修士(1987年3月 早稲田大学)

J-GLOBAL ID
200901010817271379
researchmap会員ID
1000162536

研究キーワード

 2

論文

 11
  • Yoshiyuki Ohyama, Migiwa Sakurai
    Tokyo Journal of Mathematics 46(1) 19-31 2023年6月  査読有り筆頭著者
  • Yoshiyuki OHYAMA, Migiwa SAKURAI
    Journal of the Mathematical Society of Japan 73(3) 2021年7月27日  査読有り筆頭著者
  • Yoshiyuki Ohyama, Migiwa Sakurai
    Journal of Knot Theory and Its Ramifications 28(12) 1950074-1950074 2019年10月  査読有り筆頭著者
    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) 2017年11月  査読有り
    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) 2014年4月  査読有り
    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 2010年4月  
    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 2010年4月  
    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 2009年11月  
    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年  
  • Yoshiyuki Ohyama, Harumi Yamada
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 17(7) 771-785 2008年7月  
    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.

講演・口頭発表等

 1

共同研究・競争的資金等の研究課題

 39
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社会貢献活動

 1