Inteprétations combinatoires des nombres d#Euler et de Genocchi
When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of conjugacy classes of the unitary group, using a dynamical rule inspired by the RSK algorithm. Our motivation for doing this is to develop a parallel programme, on the circle, to some recently discovered connections in random matrix theory between reflected and conditioned...
We give a pure complex variable proof of a theorem by Ismail and Stanton and apply this result in the field of integer-valued entire functions. Our proof rests on a very general interpolation result for entire functions.
Let be a simple graph. A function from the set of orientations of to the set of non-negative integers is called a continuous function on orientations of if, for any two orientations and of , whenever and differ in the orientation of exactly one edge of . We show that any continuous function on orientations of a simple graph has the interpolation property as follows: If there are two orientations and of with and , where , then for any integer such that , there are...
Let be a graph with order , size and component number . For each between and , let be the family of spanning -edge subgraphs of with exactly components. For an integer-valued graphical invariant , if is an adjacent edge transformation (AET) implies , then is said to be continuous with respect to AET. Similarly define the continuity of with respect to simple edge transformation (SET). Let and be the invariants defined by , . It is proved that both and interpolate...
In this paper, we consider the intersection graph of gamma sets in the total graph on ℤₙ. We characterize the values of n for which is complete, bipartite, cycle, chordal and planar. Further, we prove that is an Eulerian, Hamiltonian and as well as a pancyclic graph. Also we obtain the value of the independent number, the clique number, the chromatic number, the connectivity and some domination parameters of .
In this paper we classify finite groups with disconnected intersection graphs of subgroups. This solves a problem posed by Csákány and Pollák.