Path: utzoo!utgpu!watmath!maytag!watdcsu!swartz From: swartz@watdcsu.waterloo.edu ( SWARTZ SJ - COMBINATORICS Swartz OPT. ) Newsgroups: uw.talks Subject: C&O Seminar Dr. D. Wagner, University of Waterloo Keywords: Total Positivity in Combinatorics Message-ID: <6374@watdcsu.waterloo.edu> Date: 25 Sep 89 12:59:09 GMT Distribution: uw Organization: U of Waterloo, Ontario Lines: 60 C & O SEMINAR ============================================= |DATE: Friday, September 29, 1989 | | | |TIME: 3:30 p.m. | | | |PLACE: MC5158 | | | |SPEAKER: Dr. David Wagner | | University of Waterloo | | | |TITLE: Total Positivity in Combinatorics | |============================================| ABSTRACT Total positivity is a strong condition on a matrix with many applications in analysis. A deep theorem due to Aissen, Edrei, Schoenberg and Whitney characterizes the generating functions of totally positive Toeplitz matrices. We will discuss this result and applications of it to two kinds of generat- ing functions which arise in enumerative combinator- ics: partition polynomials of set systems, and order polynomials of partially ordered sets. In particular we will establish log-concavity of many combinatorial sequences. September 22, 1989