Generalized parking functions, descent numbers, and chain polytopes of ribbon posets
| dc.creator | Chebikin, Denis | |
| dc.creator | Postnikov, Alexander | |
| dc.date | 2008-06-03 | |
| dc.date.accessioned | 2026-07-07T09:42:23Z | |
| dc.date.available | 2026-07-07T09:42:23Z | |
| dc.description | We consider the inversion enumerator I_n(q), which counts labeled trees or, equivalently, parking functions. This polynomial has a natural extension to generalized parking functions. Substituting q = -1 into this generalized polynomial produces the number of permutations with a certain descent set. In the classical case, this result implies the formula I_n(-1) = E_n, the number of alternating permutations. We give a combinatorial proof of these formulas based on the involution principle. We also give a geometric interpretation of these identities in terms of volumes of generalized chain polytopes of ribbon posets. The volume of such a polytope is given by a sum over generalized parking functions, which is similar to an expression for the volume of the parking function polytope of Pitman and Stanley. | |
| dc.description | 11 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0806.0440 | |
| dc.identifier | http://arxiv.org/abs/0806.0440 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162163 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A19, 52B05 | |
| dc.title | Generalized parking functions, descent numbers, and chain polytopes of ribbon posets | |
| dc.type | text |