On signed Young permutation modules and signed p-Kostka numbers

On p-Kostka numbers and Young modules

The combinatorial properties of Young modules corresponding to maximal Young subgroups are studied: an explicit formula for p-Kostka numbers is given, and as applications, the ordinary characters of Young modules are described and a branching rule for Young modules is determined. Moreover, for certain n-part partitions the reduction formulas for p-Kostka numbers given in A. Henke, S. Koenig [Re...

Computational Complexity on Signed Numbers

This paper presents a new representation of natural numbers and discusses its consequences for computability and computational complexity. The paper argues that the introduction of the first Peano axiom in the traditional definition of natural numbers is not essential. It claims that natural numbers remain usable in traditional ways without assuming the existence of at least one natural number....

Signed domination and signed domatic numbers of digraphs

Let D be a finite and simple digraph with the vertex set V (D), and let f : V (D) → {−1, 1} be a two-valued function. If∑ x∈N[v] f(x) ≥ 1 for each v ∈ V (D), where N[v] consists of v and all vertices of D from which arcs go into v, then f is a signed dominating function on D. The sum f(V (D)) is called the weight w(f) of f . The minimum of weights w(f), taken over all signed dominating function...

Upper Binomial Posets and Signed Permutation Statistics

On Signed Edge Domination Numbers of Trees

The signed edge domination number of a graph is an edge variant of the signed domination number. The closed neighbourhood NG[e] of an edge e in a graph G is the set consisting of e and of all edges having a common end vertex with e. Let f be a mapping of the edge set E(G) of G into the set {−1, 1}. If ∑ x∈N [e] f(x) 1 for each e ∈ E(G), then f is called a signed edge dominating function on G. T...