Vol. 248, No. 1, 2010

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ISSN: 0030-8730
Expressions for Catalan Kronecker products

Andrew A. H. Brown, Stephanie van Willigenburg and Mike Zabrocki

Vol. 248 (2010), No. 1, 31–48
Abstract

We give some elementary manifestly positive formulas for the Kronecker products s(d,d) s(d+k,dk). These formulas demonstrate some fundamental properties of the Kronecker coefficients, and we use them to deduce a number of enumerative and combinatorial results.

Keywords
Catalan number, Kronecker coefficient, Kronecker product, Schur function, symmetric function
Mathematical Subject Classification 2000
Primary: 05E05
Secondary: 05E10, 20C30, 20C33
Milestones
Received: 18 August 2009
Accepted: 13 August 2010
Published: 1 October 2010
Authors
Andrew A. H. Brown
Department of Mathematics
University of British Columbia
Vancouver, BC V6T 1Z2
Canada
Department of Combinatorics and Optimization
University of Waterloo
Waterloo, ON N2L 3G1
Canada
Stephanie van Willigenburg
Department of Mathematics
University of British Columbia
Vancouver, BC V6T 1Z2
Canada
Mike Zabrocki
Department of Mathematics and Statistics
York University
Toronto, ON M3J 1P3
Canada
http://garsia.math.yorku.ca/~zabrocki/