Combinatorics Seminar: Pattern Posets and Poset Fibrations

Seminar | September 25 | 12:10-1 p.m. | 939 Evans Hall

 Jason Smith, University of Strathclyde

 Department of Mathematics

A pattern poset is a poset of combinatorial objects, with a partial order s< t if s occurs in t for some notion of occurrence. For example, the poset of words where s< t if s occurs as a subword of t. A variety of such pattern posets have been studied independently on words, permutations, graphs, Dyck paths, etc. Moreover, many of these posets have similar results relating to their Möbius function and topology. We introduce a general approach to studying these posets and prove results on their structure using the theory of poset fibrations, that is, surjective order preserving maps between posets. No prior knowledge is assumed on either of these topics.