Results 31 to 40 of about 3,811 (236)
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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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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Flag Gromov-Witten invariants via crystals [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We apply ideas from crystal theory to affine Schubert calculus and flag Gromov-Witten invariants. By defining operators on certain decompositions of elements in the type-$A$ affine Weyl group, we produce a crystal reflecting the internal structure of ...
Jennifer Morse, Anne Schilling
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Symmetric Fundamental Expansions to Schur Positivity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We consider families of quasisymmetric functions with the property that if a symmetric function f is a positive sum of functions in one of these families, then f is necessarily a positive sum of Schur functions.
Austin Roberts
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Transactions of the American Mathematical Society, 1994 A new family of symmetric functions is considered. These functions are analogous to the classical Schur functions, but depend on an integer modulus p ⩾
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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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Quasisymmetric Schur functions and modules of the $0$-Hecke algebra [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We define a $0$-Hecke action on composition tableaux, and then use it to derive $0$-Hecke modules whose quasisymmetric characteristic is a quasisymmetric Schur function.
Vasu Tewari, Stephanie van Willigenburg
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A diagrammatic approach to Kronecker squares [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 In this paper we improve a method of Robinson and Taulbee for computing Kronecker coefficients and show that for any partition $\overline{ν}$ of $d$ there is a polynomial $k_{\overline{ν}}$ with rational coefficients in variables $x_C$, where $C$ runs ...
Ernesto Vallejo
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Schur Functions and Inner Functions on the Bidisc
Computational Methods and Function Theory, 2022 We study representations of inner functions on the bidisc from a fractional linear transformation point of view, and provide sufficient conditions, in terms of colligation matrices, for the existence of two-variable inner functions. Here the sufficient conditions are not necessary in general, and we prove a weak converse for rational inner functions ...
Debnath, Ramlal, Sarkar, Jaydeb
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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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