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Expressions for
Catalan Kronecker products
Andrew A. H. Brown, Stephanie van Willigenburg and Mike Zabrocki |
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Vol. 248 (2010), No. 1, 31–48
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Abstract |
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We give some elementary manifestly positive formulas for the Kronecker products s(d,d) ∗ s(d+k,d−k). 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
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Mathematical Subject Classification 2000
Primary: 05E05
Secondary: 05E10, 20C30, 20C33
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Milestones
Received: 18 August 2009
Accepted: 13 August 2010
Published: 1 October 2010
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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 |
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| Mike Zabrocki | |
| Department of Mathematics and
Statistics York University Toronto, ON M3J 1P3 Canada |
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| http://garsia.math.yorku.ca/~zabrocki/ | |
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