Joint equidistributions of mesh patterns 123 and 321 with symmetric and minus-antipodal shadings

2024/12/31 by Shuzhen Lv, Lv, Shuzhen, Philip B. Zhang +1 · 2 citations
Computer Science · Engineering · #05A05 #05A15 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.2501.00357

openalex publication_date 2024/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

In this paper, we extend recent results by Lv and Kitaev by proving 20 (out of 22 possible) joint equidistributions of mesh patterns 123 and 321 with symmetric shadings, as well as all 36 joint equidistributions of these patterns with minus-antipodal shadings. Our results link several joint equidistributions of mesh patterns to various integer sequences, including unsigned Stirling numbers of the first kind, harmonic numbers, and the numbers of inversion sequences avoiding a certain vincular pattern studied by Lin and Yan.

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• On fourteen equidistribution conjectures of Lv and Zhang and monotone mesh patterns with corner shadings
• Joint equidistributions of mesh patterns 123 and 132 with minus antipodal shadings

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