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math.CO2024
On (joint) equidistributions of mesh patterns 123 and 132 with symmetric shadings
Sergey Kitaev, Shuzhen Lv
A notable problem within permutation patterns that has attracted considerable attention in literature since 1973 is the search for a bijective proof demonstrating that 123-avoiding…
math.CO2024★ 4 cited
Distribution of maxima and minima statistics on alternating permutations, Springer numbers, and avoidance of flat POPs
Tian Han, Sergey Kitaev, Philip B. Zhang
In this paper, we find distributions of the left-to-right maxima, right-to-left maxima, left-to-right minima and right-to-left-minima statistics on up-down and down-up permutations…
math.CO2024
On (shape-)Wilf-equivalence of certain sets of (partially ordered) patterns
Alexander Burstein, Tian Han, Sergey Kitaev +1
We prove a conjecture of Gao and Kitaev on Wilf-equivalence of sets of patterns {12345,12354} and {45123,45213} that extends the list of 10 related conjectures proved in the litera…