Toward the Schur expansion of Macdonald polynomials
The electronic journal of combinatorics, Tome 25 (2018) no. 2
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.
DOI :
10.37236/7419
Classification :
05E05, 05A15, 05A19, 05A30, 33D52
Mots-clés : Macdonald polynomials, dual equivalence, Schur positivity
Mots-clés : Macdonald polynomials, dual equivalence, Schur positivity
Affiliations des auteurs :
Sami Assaf 1
@article{10_37236_7419,
author = {Sami Assaf},
title = {Toward the {Schur} expansion of {Macdonald} polynomials},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {2},
doi = {10.37236/7419},
zbl = {1388.05187},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7419/}
}
Sami Assaf. Toward the Schur expansion of Macdonald polynomials. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/7419
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