Honeycombs for Hall Polynomials
Copyright policy )Honeycombs for Hall Polynomials
We propose a new formulation of Hall polynomials in terms of honeycombs, which were previously introduced in the context of the Littlewood–Richardson rule. We prove a Pieri rule and associativity for our honeycomb formula, thus showing equality with Hall polynomials. Our proofs are linear algebraic in nature, extending nontrivially the corresponding bijective results for ordinary Littlewood–Richardson coefficients [A. Knutson, T. Tao, C. Woodward, 2004].
- University of Melbourne Australia
Pieri rule, Symmetric functions and generalizations, Honeycombs, Hall polynomials, 510, 004, excavation moves, fugacity, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
Pieri rule, Symmetric functions and generalizations, Honeycombs, Hall polynomials, 510, 004, excavation moves, fugacity, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
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