Two Vignettes On Full Rook Placements
Combinatorics
2013-10-24 v1
Abstract
Using bijections between pattern-avoiding permutations and certain full rook placements on Ferrers boards, we give short proofs of two enumerative results. The first is a simplified enumeration of the 3124, 1234-avoiding permutations, obtained recently by Callan via a complicated decomposition. The second is a streamlined bijection between 1342-avoiding permutations and permutations which can be sorted by two increasing stacks in series, originally due to Atkinson, Murphy, and Ru\v{s}kuc.
Cite
@article{arxiv.1310.6073,
title = {Two Vignettes On Full Rook Placements},
author = {Jonathan Bloom and Vince Vatter},
journal= {arXiv preprint arXiv:1310.6073},
year = {2013}
}
Comments
9 pages, 4 figures