Equidistribution of (X,Y)-descents, (X,Y)-adjacent pairs, and (X,Y)-place-value pairs on permutations
| dc.creator | Deutsch, Emeric | |
| dc.creator | Kitaev, Sergey | |
| dc.creator | Remmel, Jeffrey | |
| dc.date | 2009-03-14 | |
| dc.date.accessioned | 2026-07-07T12:52:43Z | |
| dc.date.available | 2026-07-07T12:52:43Z | |
| dc.description | An $(X,Y)$-descent in a permutation is a pair of adjacent elements such that the first element is from $X$, the second element is from $Y$, and the first element is greater than the second one. An $(X,Y)$-adjacency in a permutation is a pair of adjacent elements such that the first one is from $X$ and the second one is from $Y$. An $(X,Y)$-place-value pair in a permutation is an element $y$ in position $x$, such that $y$ is in $Y$ and $x$ is in $X$. It turns out, that for certain choices of $X$ and $Y$ some of the three statistics above become equidistributed. Moreover, it is easy to derive the distribution formula for $(X,Y)$-place-value pairs thus providing distribution for other statistics under consideration too. This generalizes some results in the literature. As a result of our considerations, we get combinatorial proofs of several remarkable identities. We also conjecture existence of a bijection between two objects in question preserving a certain statistic. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0903.2555 | |
| dc.identifier | http://arxiv.org/abs/0903.2555 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223385 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 | |
| dc.title | Equidistribution of (X,Y)-descents, (X,Y)-adjacent pairs, and (X,Y)-place-value pairs on permutations | |
| dc.type | text |