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Frontiers in Artificial Intelligence, 2022 Group Equivariant Operators (GEOs) are a fundamental tool in the research on neural networks, since they make available a new kind of geometric knowledge engineering for deep learning, which can exploit symmetries in artificial intelligence and reduce ...
Francesco Conti +7 more
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New Inequalities and Generalizations for Symmetric Means Induced by Majorization Theory
Axioms, 2022 In this paper, the authors study new inequalities and generalizations for symmetric means and give new proofs for some known results by applying majorization theory.
Huan-Nan Shi, Wei-Shih Du
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Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We consider the graded Hopf algebra $NCSym$ of symmetric functions with non-commutative variables, which is analogous to the algebra $Sym$ of the ordinary symmetric functions in commutative variables.
Anouk Bergeron-Brlek
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On the correlation of symmetric functions [PDF]
Mathematical Systems Theory, 1996 N ...
Cai, Jin-Yi +2 more
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Weakly symmetric functions on spaces of Lebesgue integrable functions
Karpatsʹkì Matematičnì Publìkacìï, 2022 In this work, we present the notion of a weakly symmetric function. We show that the subset of all weakly symmetric elements of an arbitrary vector space of functions is a vector space.
T.V. Vasylyshyn, V.A. Zahorodniuk
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Hopf algebras and the logarithm of the S-transform in free probability ― Extended abstract [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 This document is an extended abstract of the paper `Hopf algebras and the logarithm of the S-transform in free probability' in which we introduce a Hopf algebraic approach to the study of the operation $\boxtimes$ (free multiplicative convolution) from ...
Mitja Mastnak, Alexandru Nica
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A Symmetric Function of Increasing Forests
Forum of Mathematics, Sigma, 2021 For an indifference graph G, we define a symmetric function of increasing spanning forests of G. We prove that this symmetric function satisfies certain linear relations, which are also satisfied by the chromatic quasisymmetric function and unicellular $\
Alex Abreu, Antonio Nigro
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Decomposing Bivariate Symmetric Density Function into Three Symmetric Structures. [PDF]
The Egyptian Statistical Journal, 1997 Tomizawa, Seo and Minaguchi (1996) gave a decomposition of bivariate symmetric density function. This note gives another decomposition. It is shown that the density function is symmetric if and only if it is quasi-symmetric, conditional marginal ...
Sadao Tomizawa, Tomono Konuma
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$H$-Chromatic Symmetric Functions [PDF]
The Electronic Journal of Combinatorics, 2022 We introduce $H$-chromatic symmetric functions, $X_{G}^{H}$, which use the $H$-coloring of a graph $G$ to define a generalization of Stanley's chromatic symmetric functions. We say two graphs $G_1$ and $G_2$ are $H$-chromatically equivalent if $X_{G_1}^{H} = X_{G_2}^{H}$, and use this idea to study uniqueness results for $H$-chromatic symmetric ...
Nancy Mae Eagles +4 more
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Higher order symmetric duality for multiobjective fractional programming problems over cones [PDF]
Yugoslav Journal of Operations Research, 2022 This article studies a pair of higher order nondifferentiable symmetric fractional programming problem over cones. First, higher order cone convex function is introduced.
Kaur Arshpreet, Sharma Mahesh Kumar
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