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5. On derivatives of planar mappings and their connections to complete mappingsAmela Muratović-Ribić, Enes Pašalić, 2018, izvirni znanstveni članek Opis: Given are necessary conditions for a permutation polynomial to be the derivative of a planar mapping. These conditions are not sufficient and there might exist permutation polynomials which are not derivatives of some planar mapping satisfying these conditions. For the first time we show that there is a close connection between two seemingly unrelated structures, namely planar and complete mappings. It is shown that any planar mapping induces a sequence of complete mappings having some additional interesting properties. Furthermore, a class of almost planar mappings over extension fields is introduced having the property that its derivatives are permutations in most of the cases. This class of functions then induces many infinite classes of complete mappings (permutations) as well.
Ključne besede: planar mapping, derivatives, complete mappings, permutation polynomials
Objavljeno v RUP: 19.12.2018; Ogledov: 2201; Prenosov: 243
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6. Odd extensions of transitive groups via symmetric graphs - The cubic caseKlavdija Kutnar, Dragan Marušič, 2018, izvirni znanstveni članek Opis: When dealing with symmetry properties of mathematical objects, one of the fundamental questions is to determine their full automorphism group. In this paper this question is considered in the context of even/odd permutations dichotomy. More precisely: when is it that the existence of automorphisms acting as even permutations on the vertex set of a graph, called even automorphisms, forces the existence of automorphisms that act as odd permutations, called odd automorphisms. As a first step towards resolving the above question, complete information on the existence of odd automorphisms in cubic symmetric graphs is given.
Ključne besede: automorphism group, arc-transitive, even permutation, odd permutation, cubic symmetric graph
Objavljeno v RUP: 19.11.2018; Ogledov: 2087; Prenosov: 198
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7. Imprimitive permutations in primitive groupsJoao Araújo, J. P. Araújo, Peter J. Cameron, Edward Dobson, A. Hulpke, P. Lopes, 2017, izvirni znanstveni članek Ključne besede: primitive groups, imprimitive groups, GAP, permutation type
Objavljeno v RUP: 21.02.2018; Ogledov: 2960; Prenosov: 251
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8. Odd automorphisms in vertex-transitive graphsAdemir Hujdurović, Klavdija Kutnar, Dragan Marušič, 2016, izvirni znanstveni članek Opis: An automorphism of a graph is said to be even/odd if it acts on the set of vertices as an even/odd permutation. In this article we pose the problem of determining which vertex-transitive graphs admit odd automorphisms. Partial results for certain classes of vertex-transitive graphs, in particular for Cayley graphs, are given. As a consequence, a characterization of arc-transitive circulants without odd automorphisms is obtained.
Ključne besede: graph, vertex-transitive, automorphism group, even permutation, odd permutation
Objavljeno v RUP: 15.11.2017; Ogledov: 2292; Prenosov: 100
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10. Minimal normal subgroups of transitive permutation groups of square-free degreeEdward Dobson, Aleksander Malnič, Dragan Marušič, Lewis A. Nowitz, 2007, izvirni znanstveni članek Opis: It is shown that a minimal normal subgroup of a transitive permutation group of square-free degree in its induced action is simple and quasiprimitive, with three exceptions related to ▫$A_5$▫, ▫$A_7$▫, and PSL(2,29). Moreover, it is shown that a minimal normal subgroup of a 2-closed permutation group of square-free degree in its induced action is simple. As an almost immediate consequence, it follows that a 2-closed transitive permutation group of square-free degree contains a semiregular element of prime order, thus giving a partial affirmative answer to the conjecture that all 2-closed transitive permutation groups contain such an element (see [D. Marušic, On vertex symmetric digraphs,Discrete Math. 36 (1981) 69-81; P.J. Cameron (Ed.), Problems from the fifteenth British combinatorial conference, Discrete Math. 167/168 (1997) 605-615]).
Ključne besede: mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graph
Objavljeno v RUP: 03.04.2017; Ogledov: 2406; Prenosov: 89
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