The results obtained in "A distributive lattice structure connecting Dyck paths, noncrossing partitions and 312-avoiding permutations" (Order, 22 (2005) 311-328) are transferred on Motzkin and Schröder paths. In particular, it is shown that the classes of permutations simultaneously avoiding the generalized patterns 3-12 and k-(k-1)(k-2)···21 are distributive lattices with the order induced by the strong Bruhat order (for every k greater than 1).
Some order-theoretic properties of the Motzkin and Schröder families / Bernini, Antonio; Ferrari, Luca. - STAMPA. - (2006), pp. 1-6. (Intervento presentato al convegno Permutation Patterns 2006 tenutosi a Reykjavik (Iceland) nel 12-16 giugno 2006).
Some order-theoretic properties of the Motzkin and Schröder families
BERNINI, ANTONIO;FERRARI, LUCA
2006
Abstract
The results obtained in "A distributive lattice structure connecting Dyck paths, noncrossing partitions and 312-avoiding permutations" (Order, 22 (2005) 311-328) are transferred on Motzkin and Schröder paths. In particular, it is shown that the classes of permutations simultaneously avoiding the generalized patterns 3-12 and k-(k-1)(k-2)···21 are distributive lattices with the order induced by the strong Bruhat order (for every k greater than 1).
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