Toufik Mansour, University of Haifa

Abstract

​​​​An ascent sequence is a sequence a1a2 · · · an consisting of non-negative integers satisfying a1 = 0 and for 1 < i ≤ n, ai ≤ asc(a1a2 · · · ai−1) + 1, where asc(a1a2 · · · ak) is the number of ascents in the sequence a1a2 · · · ak. We say that two sets of patterns B and C are A-Wilf-equivalent if the number of ascent sequences of length n that avoid B equals the number of ascent sequences of length n that avoid C, for all n ≥ 0. In this talk, we show that the number awk of A-Wilf-equivalence classes of k length-3 patterns is given by aw1 = 9(Duncan and Steingr´ımsson), aw2 = 35(Baxter and Pudwell), aw3 = 62, aw4 = 74, aw5 = 61, aw6 = 47, aw7 = 35, aw8 = 25, aw9 = 18, aw10 = 12, aw11 = 7, aw12 = 3, aw13 = 1.

Based on joint work with David Callan.
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Link to video: https://vimeo.com/1058786271?share=copy

Presented Via Zoom: https://rutgers.zoom.us/j/91865817691

Password: 6564120420

For further information see: https://sites.math.rutgers.edu/~zeilberg/expmath/