2009/03/30 by Allan Berele, Berele, Allan, Bridget Eileen Tenner +1
Mathematics · #05E05 (Primary) 05E10 (Secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.0903.5306
openalex publication_date 2009/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.