Skip to Main content Skip to Navigation
Conference papers

Linear time equivalence of Littlewood―Richardson coefficient symmetry maps

Abstract : Benkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the Littlewood―Richardson coefficient conjugation symmetry, i.e. $c_{\mu, \nu}^{\lambda} =c_{\mu^t,\nu^t}^{\lambda ^t}$. Tableau―switching provides an algorithm to produce such a bijective proof. Fulton has shown that the White and the Hanlon―Sundaram maps are versions of that bijection. In this paper one exhibits explicitly the Yamanouchi word produced by that conjugation symmetry map which on its turn leads to a new and very natural version of the same map already considered independently. A consequence of this latter construction is that using notions of Relative Computational Complexity we are allowed to show that this conjugation symmetry map is linear time reducible to the Schützenberger involution and reciprocally. Thus the Benkart―Sottile―Stroomer conjugation symmetry map with the two mentioned versions, the three versions of the commutative symmetry map, and Schützenberger involution, are linear time reducible to each other. This answers a question posed by Pak and Vallejo.
Complete list of metadata

Cited literature [34 references]  Display  Hide  Download

https://hal.inria.fr/hal-01185417
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 20, 2015 - 11:08:42 AM
Last modification on : Tuesday, March 7, 2017 - 3:04:25 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 9:52:23 AM

File

dmAK0111.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01185417, version 1

Collections

Citation

Olga Azenhas, Alessandro Conflitti, Ricardo Mamede. Linear time equivalence of Littlewood―Richardson coefficient symmetry maps. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.127-144. ⟨hal-01185417⟩

Share

Metrics

Record views

124

Files downloads

696