Bijections from Dyck paths to 321-avoiding permutations revisited
| dc.creator | Callan, David | |
| dc.date | 2007-11-16 | |
| dc.date.accessioned | 2026-07-07T08:43:35Z | |
| dc.date.available | 2026-07-07T08:43:35Z | |
| dc.description | There are (at least) three bijections from Dyck paths to 321-avoiding permutations in the literature, due to Billey-Jockusch-Stanley, Krattenthaler, and Mansour-Deng-Du. How different are they? Denoting them B,K,M respectively, we show that M = B \circ L = K \circ L' where L is the classical Kreweras-Lalanne involution on Dyck paths and L', also an involution, is a sort of derivative of L. Thus K^{-1} \circ B, a measure of the difference between B and K, is the product of involutions L' \circ L and turns out to be a very curious bijection: as a permutation on Dyck n-paths it is an nth root of the "reverse path" involution. The proof of this fact boils down to a geometric argument involving pairs of nonintersecting lattice paths. | |
| dc.description | 15 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/0711.2684 | |
| dc.identifier | http://arxiv.org/abs/0711.2684 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142361 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 | |
| dc.title | Bijections from Dyck paths to 321-avoiding permutations revisited | |
| dc.type | text |