A Bijective Proof of a Factorization Formula for Specialized Macdonald Polynomials

作者：Loehr Nicholas A^*; Niese Elizabeth

来源：Annals of Combinatorics, 2012, 16(4): 815-828.

DOI：10.1007/s00026-012-0162-5

• Macdonald polynomials
• inversions
• q-multinomial coefficients
• bijections

Let mu and nu = (nu(1), . . . , nu (k) ) be partitions such that mu is obtained from nu by adding m parts of size r. Descouens and Morita proved algebraically that the modified Macdonald polynomials (H) over tilde (mu) (X; q, t) satisfy the identity (H) over tilde (mu)=(H) over tilde (nu)(H) over tilde ((rm)) when the parameter t is specialize to an mth root of unity. Descouens, Morita, and Numata proved this formula bijectively when r %26lt;= nu(k) and r is an element of {1, 2}. This note gives a bijective proof of the formula for all r %26lt;= nu(k) .

• 出版日期2012-12
• 单位Virginia Tech; 美国弗吉尼亚理工大学(Virginia Tech)