We describe a map Γ from the set of Dyck paths of given semilength to itself that is the analog of the Schützenberger involution on standard Young tableaux. Afterwards, we examine the behavior of Γ with respect to Knuth's correspondence between pairs of standard Young tableaux of the same shape with at most two rows and Dyck paths. Finally, we exploit the previous results to describe a bijection between the set of 321-avoiding centrosymmetric permutations of even length and the set of 321-avoiding involutions of the same length.
The Schützenberger involution over Dyck paths
CASTRONUOVO, Niccolò
2016
Abstract
We describe a map Γ from the set of Dyck paths of given semilength to itself that is the analog of the Schützenberger involution on standard Young tableaux. Afterwards, we examine the behavior of Γ with respect to Knuth's correspondence between pairs of standard Young tableaux of the same shape with at most two rows and Dyck paths. Finally, we exploit the previous results to describe a bijection between the set of 321-avoiding centrosymmetric permutations of even length and the set of 321-avoiding involutions of the same length.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.