Inversion Formulae on Permutations Avoiding 321

Electronic Journal Of Combinatorics

Pingge Chen¹ 

关键词: Pattern avoidance;    Catalan number;    Dyck path;    Generating function;   

DOI  :  

学科分类：离散数学和组合数学

来源: Electronic Journal Of Combinatorics

【 摘 要 】

We will study the inversion statistic of $321$-avoiding permutations, and obtain that the number of $321$-avoiding permutations on $[n]$ with $m$ inversions is given by\[|\mathcal {S}_{n,m}(321)|=\sum_{b \vdash m}{n-\frac{\Delta(b)}{2}\choose l(b)}.\]wher

【 授权许可】

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