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On combinatorial formulas for Macdonald polynomials [PDF]
Advances in Mathematics, 2008 A recent breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of a pair of statistics on fillings of Young diagrams. Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of so-called alcove walks; these ...
Cristian Lenart
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Macdonald polynomials and algebraic integrability
Advances in Mathematics, 2002 54 ...
Oleg Chalykh
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Macdonald polynomials for super-partitions [PDF]
Physics Letters BWe introduce generalization of famous Macdonald polynomials for the case of super-Young diagrams that contain half-boxes on the equal footing with full boxes. These super-Macdonald polynomials are polynomials of extended set of variables: usual $p_k$ variables are accompanied by anti-commuting Grassmann variables $θ_k$.
Dmitry Galakhov +2 more
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Paths and Kostka–Macdonald Polynomials [PDF]
Moscow Mathematical Journal, 2009 We give several equivalent combinatorial descriptions of the space of states for the box-ball systems, and connect certain partition functions for these models with the q-weight multiplicities of the tensor product of the fundamental representations of the Lie algebra gl(n).
Alexander Kirillov, R. Sakamoto
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Breakthroughs in the theory of Macdonald polynomials. [PDF]
Proc Natl Acad Sci U S A, 2005 In 1998, I. G. Macdonald (1) introduced a remarkable new basis for the space of symmetric functions. The elements of this basis are denoted , where λ is a partition and p, q are two free parameters. The 's, which are now called “Macdonald polynomials,” specialize to many of the well known bases for the symmetric functions, by suitable choices of the ...
Garsia A, Remmel JB.
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Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials [PDF]
Selecta Mathematica, 2022 We present several new and compact formulas for the modified and integral form of the Macdonald polynomials, building on the compact "multiline queue" formula for Macdonald polynomials due to Corteel, Mandelshtam and Williams. We also introduce a new quasisymmetric analogue of Macdonald polynomials. These quasisymmetric Macdonald polynomials refine the
Corteel, Sylvie +4 more
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Factorizations of Symmetric Macdonald Polynomials [PDF]
Symmetry, 2018 We prove many factorization formulas for highest weight Macdonald polynomials indexed by particular partitions called quasistaircases. Consequently, we prove a conjecture of Bernevig and Haldane stated in the context of the fractional quantum Hall effect theory.
Laura Colmenarejo +2 more
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Combinatorial formula for Macdonald polynomials, Bethe Ansatz, and generic Macdonald polynomials
, 2000 We give a direct proof of the combinatorial formula for interpolation Macdonald polynomials by introducing certain polynomials, which we call generic Macdonald polynomials, which depend on $d$ additional parameters and specialize to all Macdonald polynomials of degree $d$.
Andreĭ Okounkov
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Super-Macdonald Polynomials: Orthogonality and Hilbert Space Interpretation [PDF]
Communications in Mathematical Physics, 2021 The super-Macdonald polynomials, introduced by Sergeev and Veselov (Commun Math Phys 288: 653–675, 2009), generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctions of the deformed Macdonald ...
F. Atai, Martin A. Hallnäs, E. Langmann
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Multi-Macdonald polynomials [PDF]
Discrete Mathematics, 2020 We introduce Macdonald polynomials indexed by $n$-tuples of partitions and characterized by certain orthogonality and triangularity relations. We prove that they can be explicitly given as products of ordinary Macdonald polynomials depending on special alphabets.
Camilo González, Luc Lapointe
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