Combinatorial properties of permutation tableaux
Paper in proceedings, 2008

We give another construction of a permutation tableau from its corresponding permutation and construct a permutation-preserving bijection between 1-hinge and 0-hinge tableaux. We also consider certain alignment and crossing statistics on permutation tableaux that have previously been shown to be equidistributed by mapping them to patterns in related permutations. We give two direct maps on tableaux that prove the equidistribution of those statistics by exchanging some statistics and preserving the rest. Finally, we enumerate some sets of permutations that are restricted both by pattern avoidance and by certain parameters of their associated permutation tableaux.

Permutation tableaux

Permutation patterns

Author

Alexander Burstein

Howard University

Niklas Eriksen

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08; Valparaiso; Chile; 23 June 2008 through 27 June 2008

625-640

Subject Categories

Mathematics

More information

Created

12/1/2017