1. Families of association schemes on triples from two-transitive groupsJose Maria P. Balmaceda, Dom Vito A. Briones, 2025, izvirni znanstveni članek Opis: Association schemes on triples (ASTs) are ternary analogues of classical association schemes. Similar to how Schurian association schemes arise from transitive groups, ASTs arise from two-transitive groups. In this paper, we obtain the third valencies and the number of relations of the ASTs obtained from two-transitive permutation groups. Further, we obtain the intersection numbers of the ASTs produced by PΓL(k, n), PSL(2, n), AΓL(k, n), and the sporadic two-transitive groups. In particular, the ASTs from the actions of PΓL(k, n), PSL(2, n), and the sporadic groups are commutative.
Ključne besede: association scheme on triples, permutation group, ternary algebra, algebraic combinatorics
Objavljeno v RUP: 21.10.2025; Ogledov: 515; Prenosov: 8
 Celotno besedilo (417,07 KB) |
2. Upper embeddability of graphs and products of transpositions associated with edgesShuhei Tsujie, Ryo Uchiumi, 2025, izvirni znanstveni članek Opis: Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. Dénes proved that the permutation is a full cyclic permutation for any linear order if and only if the graph is a tree.
In this article, we characterize graphs having a linear order such that the associated permutation is a full cyclic permutation in terms of graph embeddings. Moreover, we give a counter example for Eden's question about an edge ordering whose associated permutation is the identity.
Ključne besede: full cyclic permutation ordering, upper-embeddable graph, 2-cell embedding, rotation system
Objavljeno v RUP: 21.10.2025; Ogledov: 383; Prenosov: 1
Celotno besedilo (324,31 KB) |
3. Edge-transitive core-free Nest graphsIstván Kovács, 2025, izvirni znanstveni članek Opis: A finite simple graph Γ is called a Nest graph if it is regular of valency 6 and admits an automorphism ρ with two orbits of the same length such that at least one of the subgraphs induced by these orbits is a cycle. We say that Γ is core-free if no non-trivial subgroup of the group generated by ρ is normal in Aut(Γ). In this paper, we show that, if Γ is edge-transitive and core-free, then it is isomorphic to one of the following graphs: the complement of the Petersen graph, the Hamming graph H(2,4), the Shrikhande graph and a certain normal 2-cover of K_{3,3} by ℤ_2^4.
Ključne besede: bicirculant, edge-transitive, primitive permutation group
Objavljeno v RUP: 10.09.2025; Ogledov: 562; Prenosov: 4
Celotno besedilo (466,20 KB) |
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8. 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: 4683; Prenosov: 286
 Povezava na celotno besedilo |
9. 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: 4008; Prenosov: 212
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10. Imprimitive permutations in primitive groupsJoao Araújo, J. P. Araújo, Peter J. Cameron, Edward Tauscher 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: 4561; Prenosov: 263
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