云亭数学讲坛2022第94讲—— 张和平教授

文章来源:数学与统计学院发布日期:2022-11-29浏览次数:10

应学院邀请,兰州大学张和平教授将在线作学术报告。

报告题目:柱形与环面格子图的共振图与匹配强迫谱

报告摘要:In a region R consisting of unit squares, a domino is the union of two adjacent squares and a (domino) tiling is a collection of dominoes with disjoint interior whose union is the region. The flip graph T(R) is defined on the set of all tilings of R such that two tilings are adjacent  if we change one to another by a flip (a 90o rotation of a pair of side-by-side dominoes). It is well-known that  T(R) is connected when R is simply connected. By using graph theoretical approach, we show that the flip graph of (2n+1)×2m quadriculated cylinder  is still connected, but  the flip graph of (2n+1)×2m quadriculated torus is disconnected and consists of exactly two isomorphic components.

For a tiling t, we associate an integer f(t), forcing number,  as the minimum number of dominoes in t that is contained in no other tilings. As an application, we obtain that the forcing numbers of all tilings in (2n+1)×2m quadriculated cylinder and torus form respectively an integer interval whose maximum value is (n+1)m.

报告时间:20221219:00

报告地点:腾讯会议:422-792-025

邀 请 人:姚海元副教授

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报告人简介

 张和平,兰州大学数学与统计学院教授(二级)、博士生导师,校学术委员会委员,院学术委员会主任。1994年获四川大学博士学位,1999年晋升教授,2001年任博士生导师,2001年获教育部“第三届高校青年教师奖”,2002年获国务院颁发的政府特殊津贴,2009年入选甘肃省领军人才(2层次),20146月当选国际数学化学科学院院士。现任中国组合数学与图论学会常务理事,中国运筹学会组合数学与图论分会常务理事。主要从事图的匹配理论、化学图论和计算机网络的研究,发表了180余篇SCI 收录学术论文,主持了国家自然科学基金项目7项,包括重点项目“应用图论”。曾在香港浸会大学、法国巴黎南大学、澳大利亚Newcastle大学、美国中田纳西州立大学、台湾中研院数学所学术访问。