Inclusion matrices and their applications
讲座名称：
Inclusion matrices and their applications
讲座时间：
2013-11-15
讲座人：
Xiang Qing
形式：
校区：
兴庆校区
实践学分：
讲座内容：
应数学与统计学院邀请，美国德拉维尔大学（University of Delaware）数学系教授Xiang Qing将于2013.11.14-17访问我校并作学术报告。
题目：Inclusion matrices and their applications
时间：2013年11月15日（周五）， 下午4：20—5:50
地点：理科楼202
摘要：Let $X$ be a set of size of $v$. Let $1\leq t\leq k\leq v$ be integers. The subset inclusion matrix $W_{t,k}(X)$ is the ${v \choose t}$ by ${v \choose k}$ matrix, whose rows are indexed by the $t$-subsets of $X$, whose columns are indexed by the $k$-subsets of $X$, and the $(T, K)$-entry of $W_{t,k}(X)$ is 1 or 0 according as $T\subseteq K$. These inclusion matrices and their $q$-analogues played an important role in design theory and extremal set theory. We will talk about results on the Smith normal forms and $p$-ranks of $W_{t,k}(X)$, and their applications to combinatorial problems. Results on $q$-analogues of these matrices will be discussed also.
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