p-competition numbers

Dimension-2 poset competition numbers and dimension-2 poset double competition numbers

LetD = (V (D), A(D)) be a digraph. The competition graph ofD, is the graphwith vertex set V (D) and edge set {uv ∈ ( V (D) 2 ) : ∃w ∈ V (D), uw, vw ∈ A(D)}. The double competition graph of D, is the graph with vertex set V (D) and edge set {uv ∈ ( V (D) 2 )

Computable p–adic Numbers

In the present work the notion of the computable (primitive recursive, polynomially time computable) p–adic number is introduced and studied. Basic properties of these numbers and the set of indices representing them are established and it is proved that the above defined fields are p–adically closed. Using the notion of a notation system introduced by Y. Moschovakis an abstract characterizatio...

The p-Stirling Numbers

The purpose of this article is to introduce p-Stirling numbers of the first and second kinds.

The competition numbers of ternary Hamming graphs

The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest numbe...

Note on competition and phylogeny numbers