Counting descent pairs with prescribed tops and bottoms |
| |
Authors: | John T Hall |
| |
Institution: | Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA |
| |
Abstract: | Given sets X and Y of positive integers and a permutation σ=σ1σ2?σn∈Sn, an (X,Y)-descent of σ is a descent pair σi>σi+1 whose “top” σi is in X and whose “bottom” σi+1 is in Y. We give two formulas for the number of σ∈Sn with s(X,Y)-descents. is also shown to be a hit number of a certain Ferrers board. This work generalizes results of Kitaev and Remmel S. Kitaev, J. Remmel, Classifying descents according to parity, math.CO/0508570; S. Kitaev, J. Remmel, Classifying descents according to equivalence , math.CO/0604455] on counting descent pairs whose top (or bottom) is equal to . |
| |
Keywords: | Permutation patterns Descents Excedences Descent tops Descent bottoms Rook placements |
本文献已被 ScienceDirect 等数据库收录! |
|