Results 1 to 10 of about 18,306 (234)
Combinatorial Formulas for Macdonald and Hall-Littlewood Polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 A 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 fillings of Young diagrams.
Cristian Lenart
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A combinatorial model for the Macdonald polynomials. [PDF]
Proc Natl Acad Sci U S A, 2004 We prove a combinatorial formula for the Macdonald polynomial H_mu(x;q,t) which had been conjectured by the first author. Corollaries to our main theorem include the expansion of H_mu(x;q,t) in terms of LLT polynomials, a new proof of the charge formula ...
Haglund J.
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Macdonald Polynomials and Multivariable Basic Hypergeometric Series [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent ...
Michael J. Schlosser
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Highest weight Macdonald and Jack Polynomials [PDF]
, 2011 Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group.
Bernevig B A +11 more
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A Conjecture about Raising Operators for Macdonald Polynomials [PDF]
, 2005 A multivariable hypergeometric-type formula for raising operators of the Macdonald polynomials is conjectured. It is proved that this agrees with Jing and Jozefiak's expression for the two-row Macdonald polynomials, and also with Lassalle and Schlosser's
Jun’ichi Shiraishi +3 more
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Quantum corner VOA and the super Macdonald polynomials [PDF]
Journal of High Energy PhysicsIn this paper, we establish a relation between the quantum corner VOA $$q{\widetilde{Y}}_{L,0,N}[\Psi ]$$ , which can be regarded as a generalization of quantum W N algebra, and Sergeev-Veselov super Macdonald polynomials.
Panupong Cheewaphutthisakun +2 more
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A bijective proof of a factorization formula for Macdonald polynomials at roots of unity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We give a combinatorial proof of the factorization formula of modified Macdonald polynomials $\widetilde{H}_{\lambda} (X;q,t)$ when $t$ is specialized at a primitive root of unity.
F. Descouens, H. Morita, Y. Numata
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Clustering properties of rectangular Macdonald polynomials [PDF]
, 2012 The clustering properties of Jack polynomials are relevant in the theoretical study of the fractional Hall states. In this context, some factorization properties have been conjectured for the $(q,t)$-deformed problem involving Macdonald polynomials.
Dunkl, Charles F., Luque, Jean-Gabriel
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Combinatorial theory of Macdonald polynomials I: proof of Haglund's formula. [PDF]
Proc Natl Acad Sci U S A, 2005 Haglund J, Haiman M, Loehr N.
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A combinatorial approach to Macdonald q, t-symmetry via the Carlitz bijection [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We investigate the combinatorics of the symmetry relation H μ(x; q, t) = H μ∗ (x; t, q) on the transformed Macdonald polynomials, from the point of view of the combinatorial formula of Haglund, Haiman, and Loehr in terms of the inv and maj statistics on ...
Maria Monks Gillespie
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