Pattern Avoidance and Young Tableaux

Zhousheng Mei, Suijie Wang
2017 unpublished
Motivated by [13, Theorem 4.1], this paper extends Lewis's bijection to a bijec-tion between a more general class L(n, k, I) of permutations and the set of standard Young tableaux of shape (k + 1) n , so the cardinality |L(n, k, I)| = f (k+1) n , is independent of the choice of I ⊆ [n]. As a consequence, we obtain some new combinatorial realizations and identities on Catalan numbers. In the end, we raise a problem on finding a bijection between L(n, k, I) and L(n, k, I) for distinct I and I .
fatcat:vwpfxl3kb5gwzbkw67kf5rbq2q