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arXiv:1903.06589 [math.CO]AbstractReferencesReviewsResources

New combinatorial interpretation of the binomial coefficients

Paul M. Rakotomamonjy, Sandrataniaina R. Andriantsoa

Published 2019-03-15Version 1

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.

Comments: 12 pages, 2 figures and 1 table
Categories: math.CO
Subjects: 05A20, 05A05
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