東北大学数理科学連携研究センター・ワークショップ
第３回代数的組合せ論「仙台勉強会」～離散構造解析を中心として～

概要：

  • Dima Pasechnik (University of Oxford)
     Using SageMath for algebraic combinatorics, in particular for strongly regular graphs
    SageMath [1] is an open-source computer algebra system, combining systems such as GAP, Singular, PARI, etc., which are glued together by a popular mainstream programming language Python. It is well-suited for rapid implementations of various combinatorial-algebraic constructions, such as block designs, Hadamard matrices, graphs, etc.---and it includes generators for many popular constructions of such objects. In particular, for each tuple of parameters in A.E.Brouwer's tables of strongly regular graphs [2] with up to 1300 vertices for which a construction is known, SageMath can generate an example of a graph with these parameters [3].
    In our lectures we will give a quick introduction to SageMath, followed by a detailed presentation of [3].
    References.
    [1] http://www.sagemath.org/
    [2] https://www.win.tue.nl/~aeb/graphs/srg/srgtab.html
    [3] https://arxiv.org/abs/1601.00181

  • Edy Tri Baskoro（Institut Teknologi Bandung）
     Some Ramsey numbers and Ramsey $(mK_2,H)$-minimal graphs
    こちら（PDF ファイル）

  • Vladimir D. Tonchev（Michigan Technological University）
    Lecture 1：Resolvable Steiner designs and maximal arcs in projective planes
    こちら（PDF ファイル）
    Lecture 2：Counting Steiner triple systems of given 3-rank
    こちら（PDF ファイル）

  • 伊藤達郎（安徽大学）
    Three Lectures on the Terwilliger algebra of a (P and Q)-polynomial association scheme
    こちら（PDF ファイル）

  • 洞彰人（北海道大学）
    Markov chains, graph spectra, and some static/dynamic scaling limits
    I will talk about how I began to get interested in spectra of graphs and then was led to beautiful collaboration with N. Obata. Furthermore I will combine them with recent developments in probability models concerning Young diagrams. Key words are cut-off phenomenon, association scheme, quantum probability, free probability, and asymptotic representation theory.

  • Hilda Assiyatun（Institut Teknologi Bandung）
     The locating-chromatic number of trees with maximum degree 3 or 4
    こちら（PDF ファイル）

  • 坂内悦子
    A survey on Euclidean designs and relative designs
    Euclidean $t$-design was introduced by Neumaier and Seidel in 1988 as a generalization of spherical designs. Euclidean t-design is a finite set in Euclidean space. We introduce the Fisher type lower bounds for the cardinality and the concept of tight $t$-design. The concept of relative $t$-design in association schemes was introduced by Delsarte in 1977 earlier than the Definition of Euclidean designs. Instead of spheres in Euclidean space we consider shells of an association scheme. Fisher type lower bound for the cardinality and the concept of tight $t$-design. We survey on the known results of both tight Euclidean designs and tight relative designs on some association schemes.

  • 坂内英一
    Spherical designs, complex spherical designs, and unitary designs
    We first give a survey on these concepts, following the three basic papers: Spherical codes and designs (Delsarte-Goethals-Seidel, 1977); Complex spherical designs and codes (Roy-Suda, 2014); Unitary designs and codes (Roy-Scott, 2009). Then in particular we comment on the paper of Roy-Suda (2014), and discuss the existence and the classification problems of "good" tight complex spherical $T$-designs (for certain $T$) coming from tight real spherical t-designs. Here, "good" means either the number of distances $s=|A(X)|$ is small, or an association scheme is naturally attached to it. The last part of this talk is based on the ongoing joint work with Takayuki Okuda (Hiroshima University), Da Zhao (Shanghai Jiao Tong University) and Yan Zhu (Shanghai University).
    • 第３回代数的組合せ論「仙台勉強会」 トップページ