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Title

A Bijective Proof of a Factorization Formula for Specialized Macdonald Polynomials

Authors

Nicholas A. Loehr
Elizabeth Niese, Marshall UniversityFollow

Document Type

Article

Publication Date

12-2012

Abstract

Let μ and ν = (ν 1, . . . , ν k ) be partitions such that μ is obtained from ν by adding m parts of sizer. Descouens and Morita proved algebraically that the modified Macdonald polynomials

H~μ(X;q,t)

satisfy the identity

H~μ=H~νH~(r^m)

when the parameter t is specialize to an mth root of unity. Descouens, Morita, and Numata proved this formula bijectively when r ≤ ν k and

r∈{1,2}.

This note gives a bijective proof of the formula for all r ≤ ν k .

Comments

This is the pre-published manuscript.

The version of record is available from the publisher at http://link.springer.com/article/10.1007%2Fs00026-012-0162-5.

Copyright © Springer Basel 2012. All rights reserved.

Recommended Citation

Loehr, N. A., & Niese, E. (2012). A bijective proof of a factorization formula for specialized Macdonald polynomials. Annals of Combinatorics, 16(4), 815-828.