### Interdisciplinary Seminar Series

Title: Multi-restricted numbers and Multi-restrained Stirling numbers

Speaker: **Ji Young Choi**, DIMACS Visiting Researcher

Date: Monday, November 8, 2010 12:00 - 1:00 pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Given a positive integer m and nonnegative integers n and k, the (n,k)-th m-restricted Stirling number of the second kind is the number of partitions of an n-set with k nonempty subsets of size less than or equal to m, and the (n,k)-th m-restrained Stirling number of the first kind is the number of permutations of an n-set with k disjoint cycles of length less than or equal to m. In this talk, their explicit formulae, recurrence relations, generating functions, and one way to extend the numbers for negative integer n and k will be presented.

Bio:

Ji Young was born in Busan, Korea, and came to the states for graduate school where she earned her Ph. D. in Mathematics at Iowa State University in 2002 with the thesis: Multi-restricted numbers and powers of permutation representations, supervised by Dr. Jonathan D. H. Smith. Ji Young is an associate professor in the Department of Mathematics at Shippensburg University of Pennsylvania and currently she is on sabbatical as a DIMACS visiting researcher. Her research interests include topics in Algebra and Combinatorics.

Slides: Multi-restricted numbers and Multi-restrained Stirling numbers