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Symmetries among Multivariate Information Measures Explored Using Möbius Operators
Entropy, 2019 Relations between common information measures include the duality relations based on Möbius inversion on lattices, which are the direct consequence of the symmetries of the lattices of the sets of variables (subsets ordered by inclusion).
David J. Galas, Nikita A. Sakhanenko
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Explicit generating series for connection coefficients [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 This paper is devoted to the explicit computation of generating series for the connection coefficients of two commutative subalgebras of the group algebra of the symmetric group, the class algebra and the double coset algebra. As shown by Hanlon, Stanley
Ekaterina A. Vassilieva
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On the Cayley graphs of symmetric group $S_4$ [PDF]
Journal of Mahani Mathematical ResearchLet $S_n$ be the symmetric group of degree $n$. In this paper, we classify non-isomorphic Cayley graphs of $S_4$ of valency 3. Moreover, we verify that there are exactly 10 non-isomorphic Cayley graphs of $S_4$ with valency 3.
Fatemeh Raei
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Symmetric difference in abelian groups [PDF]
Pacific Journal of Mathematics, 1978 A groupoid 21 = ζA; *> is called a left (resp. right) difference group if there is a binary operation + in A such that the system is an abelian group and x*y — —x + y (resp. x * y = x ~ y). A symmetric difference group is a groupoid satisfying all the identities common to both left and right difference groups.
Grätzer, G., Padmanabhan, R.
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Conjectures on the normal covering number of finite symmetric and alternating groups [PDF]
International Journal of Group Theory, 2014 Let gamma(Sn) be the minimum number of proper subgroups Hi, i = 1,...,ell, of the symmetric group Sn such that each element in Sn lies in some conjugate of one of the Hi.
Daniela Bubboloni +2 more
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Chromatic Properties of the Pancake Graphs
Discussiones Mathematicae Graph Theory, 2017 Chromatic properties of the Pancake graphs Pn, n ⩾ 2, that are Cayley graphs on the symmetric group Symn generated by prefix-reversals are investigated in the paper.
Konstantinova Elena
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Some properties of Square element graphs over semigroups
AKCE International Journal of Graphs and Combinatorics, 2020 The Square element graph over a semigroup is a simple undirected graph whose vertex set consists precisely of all the non-zero elements of , and two vertices are adjacent if and only if either or belongs to the set , where 1 is the identity of the ...
Bijon Biswas +3 more
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On the Genus of Symmetric Groups [PDF]
Transactions of the American Mathematical Society, 1981 A new method for determining genus of a group is described. It involves first getting a bound on the sizes of the generating set for which the corresponding Cayley graph could have smaller genus. The allowable generating sets are then examined by methods of computing average face sizes and by voltage graph techniques to find the best embeddings.
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