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Cyclotomic Polynomials, Symmetric Polynomials, and a Generalization of Euler's Totient Function
Mathematics Magazine, 2012We introduce a generalization of Euler's totient function that, when applied to an integer n ≥ 2, can be written as a polynomial in the prime factors of n.
null Julian Freed-Brown +3 more
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Generation of Gray code ordered Walsh functions by symmetric and shift copies
1993 IEEE International Symposium on Circuits and Systems, 2002A new theoretical formulation of Gray code ordered Walsh functions by symmetric and shift copies is presented. The formulation is based on different operations on matrices together with some symmetry features of Gray code ordered Walsh functions. The method by which the Walsh functions are ordered is determined mainly by convenience.
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Using Gram matrices and residues to generate symmetric functions
2012In this paper we argue for the use of a symmetric bilinear map S on Qn+1 as a means of producing and manipulating symmetric functions; using certain vectors of rational functions we can produce Schur functions. We define S as the determinant of a specific Gram matrix, whose elements are the result of an antisymmetric bilinear map on Q as well as a ...
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New Inequalities and Generalizations for Symmetric Means Induced by Majorization Theory
Axioms, 2022Huan-nan Shi, Wei–Shih Du
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The Yang-Baxter equation, symmetric functions, and Schubert polynomials
Discrete Mathematics, 1996Sergey Fomin
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Two-dimensional symmetric and antisymmetric generalizations of sine functions
Journal of Mathematical Physics, 2010Jiří Hrivnák, Lenka Motlochová
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A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions
Letters in Mathematical Physics, 1996Satoru Odake
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