According to Shapley’s game-theoretical result, there exists a unique game value of finite cooperative games that satisfies axioms on additivity, efficiency, null-player property and symmetry. The original setting requires symmetry with respect to arbitrary permutations of players. We analyze the consequences of weakening the symmetry axioms and study quasi-values that are symmetric with respec...

If the permutation action ρI is transitive, all factors Xi are quasiisometric to each other, and the restricted quasi-actions Gi y Xi are quasi-conjugate (when identifying different stabilizers Gi by inner automorphisms of G). The main result of this note is that in this case any of the quasi-actions Gi y Xi determines ρ up to quasi-conjugacy, and moreover any quasi-conjugacy class may arise as...

For a finite group G, we denote by μ(G) and c(G), the minimal degree of faithful permutation representation G quasi-permutation matrices over complex field C respectively. In this paper, examine c(G) for VZ-groups Camina p-groups.

In collaboration with João Araújo and others, I have been thinking about relations between permutation groups and transformation semigroups. In particular, what properties of a permutation group G on a set Ω guarantee that, if f is any non-permutation on Ω (or perhaps any non-permutation of rank k), then the transformation semigroup 〈G, f〉 has specified properties. There is far too much to summ...

We prove that a hereditary property of cographs has bounded linear cliquewidth if and only if it does not contain all quasi-threshold graphs or their complements. The proof borrows ideas from the enumeration of permutation classes, and the similarities between these two strands of investigation lead us to a conjecture relating the graph properties of bounded linear clique-width to permutation c...

We investigate parallel analysis (PA), a selection rule for the number-of-factors problem, from the point of view of permutation assessment. The idea of applying permutation test ideas to PA leads to a quasi-inferential, non-parametric version of PA which accounts not only for finite-sample bias but sampling variability as well. We give evidence, however, that quasi-inferential PA based on norm...

We consider well-quasi-order for classes of permutation graphs which omit both a path and a clique. Our principle result is that the class of permutation graphs omitting P5 and a clique of any size is well-quasi-ordered. This is proved by giving a structural decomposition of the corresponding permutations. We also exhibit three infinite antichains to show that the classes of permutation graphs ...