Related papers: Decomposition of tournament limits

We state and prove some counting formulas relating to cliques in the distant graphs of projective lines over finite rings. As a preliminary to this, we prove a decomposition theorem for the graphs in terms of the direct-product…

Real world tournaments are almost always intransitive. Recent works have noted that parametric models which assume $d$ dimensional node representations can effectively model intransitive tournaments. However, nothing is known about the…

The theory of graphons is an important tool in understanding properties of large networks. We investigate a power-law random graph model and cast it in the graphon framework. The distinctively different structures of the limit graph are…

A tournament on 8 or more vertices may be intrinsically linked as a directed graph. We begin the classification of intrinsically linked tournaments by examining their score sequences. While many distinct tournaments may have the same score…

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

We prove that for every fixed $k$, the number of occurrences of the transitive tournament $Tr_k$ of order $k$ in a tournament $T_n$ on $n$ vertices is asymptotically minimized when $T_n$ is random. In the opposite direction, we show that…

We show that all the tangles in a finite graph or matroid can be distinguished by a single tree-decomposition that is invariant under the automorphisms of the graph or matroid. This comes as a corollary of a similar decomposition theorem…

We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain…

We consider vertex decompositions of (di)graphs which appear in Automata Theory, and establish some their properties. Then we apply them to the problem of forbidden subgraphs.

We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…

We present an easy structure theorem for graphs which do not admit an immersion of the complete graph. The theorem motivates the definition of a variation of tree decompositions based on edge cuts instead of vertex cuts which we call…

In comparing well-known CRDTs representing sets that can grow and shrink, we find caveats. In one, the removal of an element cannot be reliably undone. In another, undesirable states are attainable, such as when an element is present -1…

Generalizations of Redfield's master theorem and superposition theorem are proved by using decomposition of the tensor product of several induced monomial representations of the symmetric group $S_d$ into transitive constituents. As direct…

We give a sufficient criterion for a lower bound of the cactus rank of a tensor. Then we refine that criterion in order to be able to give an explicit sufficient condition for a non-redundant decomposition of a tensor to be minimal and…

The main result provide a common generalization for Ramsey-type theorems concerning finite colorings of edge sets of complete graphs with vertices in infinite semigroups. We capture the essence of theorems proved in different fields: for…

This paper concerns matrix decompositions in which the factors are restricted to lie in a closed subvariety of a matrix group. Such decompositions are of relevance in control theory: given a target matrix in the group, can it be decomposed…

We start an analysis of geometric properties of a structure relative to a reduct. In particular, we look at definability of groups and fields in this context. In the relatively one-based case, every definable group is isogenous to a…

The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…

We develop a technique that we call Conflict Packing in the context of kernelization, obtaining (and improving) several polynomial kernels for editing problems on dense instances. We apply this technique on several well-studied problems:…

We consider representations of tensors as sums of decomposable tensors or, equivalently, decomposition of multilinear forms into one--forms. In this short note we show that there exists a particular finite strongly orthogonal decomposition…