Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon Schur functions

By Louis J. Billera, Hugh Thomas, Stephanie van Willigenburg. 2004

71 citations recorded by the source corpus.

Abstract We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of a factorization for compositions: equivalent compositions have factorizations that differ only by reversing some of the terms. As an application, we can derive identities on certain Littlewood–Richardson coefficients. Finally, we consider the cone of symmetric functions having a nonnnegative representation in terms of the fundamental quasisymmetric basis. We show the Schur functions are among the extremes of this cone and conjecture its facets are in bijection with the equivalence classes of compositions.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9833a88dd246cf84a0faa24665ec06921f706581

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On adding a list of numbers (and other one-dependent determinantal processes) (2009, background): “The paper [3] characterizes when two ribbon skew-Schur functions are equal; analogous results for more general skew-Schur functions are in [63].”