On (joint) equidistributions of mesh patterns 123 and 132 with symmetric shadings

S Kitaev, S Lv - arxiv preprint arxiv:2408.09401, 2024 - arxiv.org
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 and …

[HTML][HTML] Combinatorial generation via permutation languages. VI. Binary trees

P Gregor, T Mütze - European Journal of Combinatorics, 2024 - Elsevier
In this paper we propose a notion of pattern avoidance in binary trees that generalizes the
avoidance of contiguous tree patterns studied by Rowland and non-contiguous tree patterns …

Distributions of mesh patterns of short lengths on king permutations

D Li, PB Zhang - arxiv preprint arxiv:2411.18131, 2024 - arxiv.org
Br\"{a} nd\'{e} n and Claesson introduced the concept of mesh patterns in 2011, and since
then, these patterns have attracted significant attention in the literature. Subsequently, in …

On (joint) equidistributions of mesh patterns 123 and 132 with symmetric shadings

S Lv, S Kitaev - Advances in Applied Mathematics, 2025 - Elsevier
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 and …

[HTML][HTML] Asymptotic behaviour of the containment of certain mesh patterns

D Govc, JP Smith - Discrete Mathematics, 2022 - Elsevier
We present some results on the proportion of permutations of length n containing certain
mesh patterns as n grows large, and give exact enumeration results in some cases. In …