Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: Another (more refined) look at the Wilf-equivalances of length 4 patterns
Speaker: Jonathan Bloom, Rutgers University
Date: Thursday, February 12, 2015 5:00pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
In this talk we will settle two recent conjectures in the area of enumerative combinatorics. First, we answer a conjecture of B. Sagan by finding a multi-statistic preserving bijection between 1423-avoiding permutations and 2413-avoiding permutations. This new bijection also generalizes a classical result, in the area of pattern avoidance, due to Stankova. In the second part of the talk, we employ the techniques used to construct the aforementioned bijection to also prove a conjecture of E. Egge from 2011. In particular, we show that certain pattern classes are, surprisingly, counted by the large Schroder numbers.