| An Involution over Dyck Paths Related with Stirling Statistics |
| Received:July 11, 2023 Revised:September 23, 2023 |
| Key Words:
involutions Dyck paths pattern peak returns
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11701420). |
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| Abstract: |
| We construct an involution over Dyck paths, which implies the distribution of statistics ``the number of peak'', ``the number of returns'' and ``the height of the last peak''. As an application, equidistributions of several Stirling statistics over 132-avoiding and $321$-avoiding permutations are presented. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2024.04.002 |
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