Surprising Symmetries in Objects Counted by Catalan Numbers

Electronic Journal Of Combinatorics

Miklós Bóna¹ 

关键词: permutations;    patterns;    plane trees;    bijection;   

DOI  :  

学科分类：离散数学和组合数学

来源: Electronic Journal Of Combinatorics

【 摘 要 】

We prove that the total number $S_{n,132}(q)$ of copies of  the pattern $q$ in all 132-avoiding permutations of length $n$ is the same for $q=231$, $q=312$, or $q=213$. We provide a combinatorial proof for this unexpected threefold symmetry. We then signi

【 授权许可】

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