Humps in Motzkin paths and standard Young tableaux in a (2,1)-hook
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 in 2009. We also give new combinatorial proofs of Regev's results, and reveal some new recurrence relations related to humps, free Motzkin paths and SYTs.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.