Results 31 to 40 of about 3,636 (229)
A generalization of $(q,t)$-Catalan and nabla operators [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We introduce non-commutative analogs of $k$-Schur functions and prove that their images by the non-commutative nabla operator $\blacktriangledown$ is ribbon Schur positive, up to a global sign.
N. Bergeron, F. Descouens, M. Zabrocki
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Schur-power convexity of integral mean for convex functions on the coordinates
Open Mathematics, 2023 In this article, we investigate the concepts of monotonicity, Schur-geometric convexity, Schur-harmonic convexity, and Schur-power convexity for the lower and upper limits of the integral mean, focusing on convex functions on coordinate axes. Furthermore,
Shi Huannan, Zhang Jing
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Equality of Schur and Skew Schur Functions [PDF]
Annals of Combinatorics, 2005 9 pages, final ...
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The symmetric KP hierarchy and affine Yangian of gl(1)
Nuclear Physics B, 2023 The symmetric functions Yλ(x) are a generalization of Schur functions Sλ(x), and Yλ(x) are symmetric about the x-axis and y-axis. As the Schur functions can be used to describe the tau functions of the KP hierarchy, in this paper, we define the symmetric
Na Wang, Ke Wu
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Elliptic Combinatorics and Markov Processes [PDF]
, 2012 We present combinatorial and probabilistic interpretations of recent results in the theory of elliptic special functions (due to, among many others, Frenkel, Turaev, Spiridonov, and Zhedanov in the case of univariate functions, and Rains in the ...
Betea, Dan Dumitru
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Noncommutative Symmetric Hall-Littlewood Polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Noncommutative symmetric functions have many properties analogous to those of classical (commutative) symmetric functions. For instance, ribbon Schur functions (analogs of the classical Schur basis) expand positively in noncommutative monomial basis ...
Lenny Tevlin
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An inequality for schur functions
Linear Algebra and its Applications, 1972 AbstractIf H is a subgroup of the symmetric group of degree n and χ is a complex character on H of degree 1, then the Schur function for H and χ is defined by dχH(Y) = ∑σϵH χ(σ) ∏i=1n yiσ(i) for any n-square matrix Y = (yij).It is shown that, if A1 is a positive definite matrix, A2 a positive semidefinite nonzero matrix, and μ1, μ2 complex numbers ...
Marcus, Marvin, Minc, Henryk
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New insights into superintegrability from unitary matrix models
Physics Letters B, 2022 Some eigenvalue matrix models possess an interesting property: one can manifestly define the basis where all averages can be explicitly calculated. For example, in the Gaussian Hermitian and rectangular complex models, averages of the Schur functions are
A. Mironov, A. Morozov, Z. Zakirova
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A relationship between rational and multi-soliton solutions of the BKP hierarchy [PDF]
, 2005 We consider a special class of solutions of the BKP hierarchy which we call $\tau$-functions of hypergeometric type. These are series in Schur $Q$-functions over partitions, with coefficients parameterised by a function of one variable $\xi$, where the ...
Orlov, A.Y., Nimmo, J.J.C.
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Generalized Schur functions and augmented Schur parameters [PDF]
, 2005 Every Schur function s(z) is the uniform limit of a sequence of finite Blaschke products on compact subsets of the open unit disk. The Blaschke products in the sequence are defined inductively via the Schur parameters of s(z).
Wanjala, Gerald, Dijksma, Aad
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