<abstract xmlns="http://www.w3.org/1999/xhtml"> We define an order relation over Sn considering the Robinson-Schensted bijection and the dominance order over Young tableaux. This order relation makes Sn(k k - 1...3 2 1) -the set of permutations of length n that avoid the pattern k k - 1...3 2 1, k ≤ n- a principal filter in Sn. We study in detail these order relations on Sn(321) and Sn(4321), finding order-isomorphisms between these sets and sets of lattice paths. </abstract>

We define an order relation over Sn considering the Robinson-Schensted bijection and the dominance order over Young tableaux. This order relation makes Sn(k k - 1...3 2 1) -the set of permutations of length n that avoid the pattern k k - 1...3 2 1, k ≤ n- a principal filter in Sn. We study in detail these order relations on Sn(321) and Sn(4321), finding order-isomorphisms between these sets and sets of lattice paths.

The dominance order for permutations

Dipartimento di Scienze Fisiche, Informatiche, Matematiche Università di Modena e Reggio Emilia Italy

Pure Mathematics and Applications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"The dominance order for permutations"}

We define an order relation over Sn considering the Robinson-Schensted bijection and the dominance order over Young tableaux. This order relation makes Sn(k k...

The dominance order for permutations

Published Online: Oct 07, 2015

Page range: 45 - 62

Received: Sep 14, 2014

DOI: https://doi.org/10.1515/puma-2015-0004

Keywords
Robinson-Schensted bijection, Dyck path, 321-avoiding permutation, Young tableau, dominance order

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The dominance order for permutations

Published Online: Oct 07, 2015

Page range: 45 - 62

Received: Sep 14, 2014

DOI: https://doi.org/10.1515/puma-2015-0004

KeywordsRobinson-Schensted bijection, Dyck path, 321-avoiding permutation, Young tableau, dominance order

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Robinson-Schensted bijection, Dyck path, 321-avoiding permutation, Young tableau, dominance order