Linearly Independent Products of Rectangularly Complementary Schur Functions

Fix a rectangular Young diagram R, and consider all the products of Schur functions ssc , where and c run over all (unordered) pairs of partitions which are complementary with respect to R. Theorem: The self-complementary products, s2 where = c, are linearly independent of all other ssc . Conjecture: The products ssc are all linearly independent.

• Type: Journal
• Year: 2002
• Where: COMBINATORICS
• Authors: Michael Kleber
• Keywords: COMBINATORICS 2002, Linearly Independent, Rectangular Young Diagram, Schur Functions