Toward the Schur Expansion of Macdonald Polynomials
Copyright policy )Toward the Schur Expansion of Macdonald Polynomials
We give an explicit combinatorial formula for the Schur expansion of Macdonald polynomials indexed by partitions with second part at most two. This gives a uniform formula for both hook and two column partitions. The proof comes as a corollary to the result that generalized dual equivalence classes of permutations are in explicit bijection with unions of standard dual equivalence classes of permutations for certain cases, establishing an earlier conjecture of the author, and suggesting that this result might be generalized to arbitrary partitions.
- University of California System United States
- University of Southern California United States
Symmetric functions and generalizations, \(q\)-calculus and related topics, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, Macdonald polynomials, dual equivalence, Combinatorics (math.CO), Schur positivity, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Combinatorial identities, bijective combinatorics
Symmetric functions and generalizations, \(q\)-calculus and related topics, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, Macdonald polynomials, dual equivalence, Combinatorics (math.CO), Schur positivity, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Combinatorial identities, bijective combinatorics
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