Humps in Motzkin Paths and Standard Young Tableaux in a (2,1)-Hook
Xiaomei Chen
School of Mathematics and Statistics
Hunan University of Science and Technology
Xiangtan 411201
China
Abstract:
We calculate the number of humps and peaks in Motzkin paths with a given
height, and calculate the number of standard Young tableaux (SYTs)
in a (2,1)-hook with the difference of the first two parts fixed,
which refine Regev’s results. We also give new bijective proofs of
Regev’s results, and reveal some new recurrence relations related to
humps, free Motzkin paths, and SYTs.
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(Concerned with sequences
A001006
A002426
A005043
A033184
A064189
A097861
A140662
A187306
A284778
A379838
A379893.)
Received January 3 2025; revised versions received January 6 2025; September 26 2025.
Published in Journal of Integer Sequences,
December 10 2025.
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