Alternating permutations and symmetric functions
| dc.creator | Stanley, Richard P. | |
| dc.date | 2006-03-21 | |
| dc.date | 2006-07-05 | |
| dc.date.accessioned | 2026-07-07T07:07:09Z | |
| dc.date.available | 2026-07-07T07:07:09Z | |
| dc.description | We use the theory of symmetric functions to enumerate various classes of alternating permutations w of {1,2,...,n}. These classes include the following: (1) both w and w^{-1} are alternating, (2) w has certain special shapes, such as (m-1,m-2,...,1), under the RSK algorithm, (3) w has a specified cycle type, and (4) w has a specified number of fixed points. We also enumerate alternating permutations of a multiset. Most of our formulas are umbral expressions where after expanding the expression in powers of a variable E, E^k is interpreted as the Euler number E_k. As a small corollary, we obtain a combinatorial interpretation of the coefficients of an asymptotic expansion appearing in Ramanujan's Lost Notebook. | |
| dc.description | 37 pages, one figure. Correction of gap in the proof of Corollary 6.4, and some further minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0603520 | |
| dc.identifier | http://arxiv.org/abs/math/0603520 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110283 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15; 05A40; 05E05 | |
| dc.title | Alternating permutations and symmetric functions | |
| dc.type | text |