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Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coefficients of a certain mock theta function studied by the first author,...
We study a particular digraph dynamical system, the so called digraph diclique operator. Dicliques have frequently appeared in the literature the last years in connection with the construction and analysis of different types of networks, for instance biochemical, neural, ecological, sociological and computer networks among others. Let be a reflexive digraph (or network). Consider and (not necessarily disjoint) nonempty subsets of vertices (or nodes) of . A disimplex of is the subdigraph...
In this paper we will describe a new class of coloring problems, arising from military frequency assignment, where we want to minimize the number of distinct -uples of colors used to color a given set of -complete-subgraphs of a graph. We will propose two relaxations based on Semi-Definite Programming models for graph and hypergraph coloring, to approximate those (generally) NP-hard problems, as well as a generalization of the works of Karger et al. for hypergraph coloring, to find good feasible...
In this paper we will describe a new class of coloring
problems, arising from military frequency assignment, where we want to
minimize the number of distinct n-uples of colors used to color a given
set of n-complete-subgraphs of a graph.
We will propose two relaxations based on
Semi-Definite Programming models for graph and hypergraph
coloring, to approximate those (generally) NP-hard problems, as well as
a generalization of the works of Karger et al. for hypergraph coloring,
to find good feasible...
Certain numerical invariants of directed graphs, analogous to the domatic number and to the total domatic number of an undirected graph, are introduced and studied.
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