Linearly Independent Products of Rectangularly Complementary Schur Functions

Details Linearly Independent Products of Rectangularly Complementary Schur Functions Linearly Independent Products of Rectangularly Complementary Schur Functions

2002-09-11

arxiv.org/abs/math/0209136v2

Electronic Journal of Combinatorics 9(1) (2002) #R39

Mathematics

Combinatorics

8 pages. Final version appearing in EJC. Formerly titled "A Theorem and a Conjecture on Rectangles and Schur Functions;" the s

Scientific paper

Fix a rectangular Young diagram R, and consider all the products of Schur functions s(mu) s(mu^c), where mu and mu^c run over all (unordered) pairs of partitions which are complementary with respect to R. Theorem: The self-complementary products, s(mu)^2 where mu=mu^c, are linearly independent of all other s(mu) s(mu^c). Conjecture: The products s(mu) s(mu^c) are all linearly independent.

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