Results 31 to 40 of about 18,484 (234)
Combinatorial Formula for the Hilbert Series of bigraded $S_n$-modules [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We introduce a combinatorial way of calculating the Hilbert series of bigraded $S_n$-modules as a weighted sum over standard Young tableaux in the hook shape case.
Meesue Yoo
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A generalization of the Kostka-Foulkes polynomials [PDF]
, 1998 Combinatorial objects called rigged configurations give rise to q-analogues of certain Littlewood-Richardson coefficients. The Kostka-Foulkes polynomials and two-column Macdonald-Kostka polynomials occur as special cases.
Kirillov, Anatol N., Shimozono, Mark
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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 ...
Haglund, James, Wilson, Andrew Timothy
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Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
Journal of High Energy Physics, 2017 We find new universal factorization identities for generalized Macdonald polynomials on the topological locus. We prove the identities (which include all previously known forumlas of this kind) using factorization identities for matrix model averages ...
Yegor Zenkevich
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Canonical Basis and Macdonald Polynomials
Advances in Mathematics, 1998 In the basic representation of $U_q(\hat{sl}(2))$ realized via the algebra of symmetric functions we compare the canonical basis with the basis of Macdonald polynomials with $q=t^2$. We show that the Macdonald polynomials are invariant with respect to the bar involution defined abstractly on the representations of quantum groups. We also prove that the
Beck, Jonathan +2 more
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Staircase Macdonald polynomials and the $q$-Discriminant [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We prove that a $q$-deformation $\mathfrak{D}_k(\mathbb{X};q)$ of the powers of the discriminant is equal, up to a normalization, to a specialization of a Macdonald polynomial indexed by a staircase partition. We investigate the expansion of $\mathfrak{D}
Adrien Boussicault, Jean-Gabriel Luque
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On Hamiltonians for Kerov functions
European Physical Journal C: Particles and Fields, 2020 Kerov Hamiltonians are defined as a set of commuting operators which have Kerov functions as common eigenfunctions. In the particular case of Macdonald polynomials, well known are the exponential Ruijsenaars Hamiltonians, but the exponential shape is not
A. Mironov, A. Morozov
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A New Generalisation of Macdonald Polynomials [PDF]
Communications in Mathematical Physics, 2017 We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters $(q,t)$ and polynomial in a further two parameters $(u,v)$. We evaluate these polynomials explicitly as a matrix product.
Alexandr Garbali +2 more
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Parabolic Refined Invariants and Macdonald Polynomials [PDF]
Communications in Mathematical Physics, 2014 77 ...
Chuang, Wu-yen +3 more
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The Classification of All Singular Nonsymmetric Macdonald Polynomials
Axioms, 2022 The affine Hecke algebra of type A has two parameters q,t and acts on polynomials in N variables. There are two important pairwise commuting sets of elements in the algebra: the Cherednik operators and the Jucys–Murphy elements whose simultaneous ...
Charles F. Dunkl
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