曹锡华代数论坛

报告人：陈北方教授（香港科技大学）

时间：2011年6月21日(周二)上午10：30-11:30

地点：闵行校区数学楼102报告厅

Title: Counting patterns and geometric measures

Abstract: In many occasions counting the number of objects of finite
sets parameterized by a family of integers gives rise to a polynomial
function of the family of the integers. For instance in graph
theory, counting the number of proper colorings of a graph by $n$
colors gives rise to the chromatic polynomial function of $n$; the
polynomial comes from the counting patterns $n^k$, the number of
colorings of a $k$ element set by $n$ colors without restriction. If
the number of elements to be counted in sets are infinite, the
ordinary counting does not make sense. However, in some occasions
the counting patters are still there, and give rise to power series
or asymptotic formulas. In this talk, I shall exhibit a number of
examples from the viewpoint of counting or measuring finite and
infinite sets with structures, including an example of interpreting
the generating function of partitions of integers as the total
measure of the Grassmannian of infinite-dimensional subspaces of the
vector space ${\Bbb K}^\infty$ over a field $\Bbb K$.