Results 61 to 70 of about 77,378 (232)
A combinatorial formula for Macdonald polynomials
Advances in Mathematics, 2011 In this paper we use the combinatorics of alcove walks to give a uniform combinatorial formula for Macdonald polynomials for all Lie types. These formulas are generalizations of the formulas of Haglund-Haiman-Loehr for Macdonald polynoimals of type GL(n).
Martha Yip, Arun Ram, Arun Ram
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Symmetry, Integrability and Geometry: Methods and Applications, 2013 We present a semi-infinite q-boson system endowed with a four-parameter boundary interaction. The n-particle Hamiltonian is diagonalized by generalized Hall-Littlewood polynomials with hyperoctahedral symmetry that arise as a degeneration of the ...
Jan Felipe van Diejen, Erdal Emsiz
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Pieri rules for Schur functions in superspace [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The Schur functions in superspace $s_\Lambda$ and $\overline{s}_\Lambda$ are the limits $q=t= 0$ and $q=t=\infty$ respectively of the Macdonald polynomials in superspace.
Miles Eli Jones, Luc Lapointe
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Deformed Macdonald-Ruijsenaars Operators and Super Macdonald Polynomials [PDF]
Communications in Mathematical Physics, 2009 It is shown that the deformed Macdonald-Ruijsenaars operators can be described as the restrictions on certain affine subvarieties of the usual Macdonald-Ruijsenaars operator in infinite number of variables. The ideals of these varieties are shown to be generated by the Macdonald polynomials related to Young diagrams with special geometry.
Alexander P. Veselov +3 more
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Macdonald Polynomials and Chromatic Quasisymmetric Functions [PDF]
The Electronic Journal of Combinatorics, 2020 We express the integral form Macdonald polynomials as a weighted sum of Shareshian and Wachs' chromatic quasisymmetric functions of certain graphs. Then we use known expansions of these chromatic quasisymmetric functions into Schur and power sum symmetric functions to provide Schur and power sum formulas for the integral form Macdonald polynomials ...
Andrew Timothy Wilson, James Haglund
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Orthogonal Polynomials of Compact Simple Lie Groups
International Journal of Mathematics and Mathematical Sciences, 2011 Recursive algebraic construction of two infinite families of polynomials in n variables is proposed as a uniform method applicable to every semisimple Lie group of rank n.
Maryna Nesterenko +2 more
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Matrix product formula for Macdonald polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2015 27 pages; typos corrected, references added and some better conventions adopted in ...
Cantini, L, de Gier, J, Wheeler, M
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Double Macdonald polynomials as the stable limit of Macdonald superpolynomials [PDF]
Journal of Algebraic Combinatorics, 2014 40 pages; v2: title and abstract changed; minor modifications in the ...
Olivier Blondeau-Fournier +2 more
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(q,t)-deformed (skew) Hurwitz τ-functions
Nuclear Physics B, 2023 We follow the general recipe for constructing commutative families of W-operators, which provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order to obtain a difference operator example that gives rise to a (q,t ...
Fan Liu +6 more
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Polynomials and Parking Functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 In a 2010 paper Haglund, Morse, and Zabrocki studied the family of polynomials $\nabla C_{p1}\dots C_{pk}1$ , where $p=(p_1,\ldots,p_k)$ is a composition, $\nabla$ is the Bergeron-Garsia Macdonald operator and the $C_\alpha$ are certain slightly modified
Angela Hicks
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