Doubly Symmetric Functions

Details Doubly Symmetric Functions Doubly Symmetric Functions

2009-03-30

arxiv.org/abs/0903.5306v1

Mathematics

Combinatorics

11 pages

Scientific paper

In this paper we introduce doubly symmetric functions, arising from the equivalence of particular linear combinations of Schur functions and hook Schur functions. We study algebraic and combinatorial aspects of doubly symmetric functions, in particular as they form a subalgebra of the algebra of symmetric functions. This subalgebra is generated by the odd power sum symmetric functions. One consequence is that a Schur function itself is doubly symmetric if and only if it is the Schur function of a staircase shape.

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