Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777513 | Journal of Combinatorial Theory, Series A | 2017 | 35 Pages |
Abstract
We continue our development of a new basis for the algebra of non-commutative symmetric functions. This basis is analogous to the basis of Schur functions for the algebra of symmetric functions, and it shares many of its wonderful properties. For instance, in this article we describe non-commutative versions of the Littlewood-Richardson rule and the Murnaghan-Nakayama rule. A surprising relation develops among non-commutative Littlewood-Richardson coefficients, which has implications to the commutative case. Finally, we interpret these new coefficients geometrically as the number of integer points inside a certain polytope.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Chris Berg, Nantel Bergeron, Franco Saliola, Luis Serrano, Mike Zabrocki,