New combinatorial interpretations of the binomial coefficients
Combinatorics
2019-04-01 v3
Abstract
Using generating functions and some trivial bijections, we show in this paper that the binomial coefficients count the set of (123,132) and (123,213)-avoiding permutations according to the number of crossings. We also define a q-tableau of power of two and prove that it counts the set of (213,312) and (132,312)-avoiding permutations according to the number of crossings.
Cite
@article{arxiv.1903.06589,
title = {New combinatorial interpretations of the binomial coefficients},
author = {Paul M. Rakotomamonjy and Sandrataniaina R. Andriantsoa},
journal= {arXiv preprint arXiv:1903.06589},
year = {2019}
}
Comments
15 pages, 2 figures and 1 table