Related papers: Complete branching rules for Specht modules

Over fields of characteristic $2$, Specht modules may decompose and there is no upper bound for the dimension of their endomorphism algebra. A classification of the (in)decomposable Specht modules and a closed formula for the dimension of…

This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…

In [Boltje,Hartmann: Permutation resolutions for Specht modules, J. Algebraic Combin. 34 (2011), 141-162], a chain complex was constructed in a combinatorial way which conjecturally is a resolution of the (dual of the) integral Specht…

Milnor patching diagram is essentially the commutative square of rings, over which gluing of finitely generated projective modules is possible in the strongest sense. Necessary and sufficient conditions for a square to be Milnor patching…

A shelling of a graph, viewed as an abstract simplicial complex that is pure of dimension 1, is an ordering of its edges such that every edge is adjacent to some other edges appeared previously. In this paper, we focus on complete bipartite…

Full strong-branching is a well-known variable selection rule that is known experimentally to produce significantly smaller branch-and-bound trees in comparison to all other known variable selection rules. In this paper, we attempt an…

Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…

In this paper we study the vertices of indecomposable Specht modules for symmetric groups. For any given indecomposable non-projective Specht module, the main theorem of the article describes a family of p-subgroups contained in its vertex.…

We classify modules and rings with some specific properties of their intersection graphs. In particular, we describe rings with infinite intersection graphs containing maximal left ideals of finite degree. This answers a question raised in…

In the present paper, complete designs of graphs are considered. The notion of (regular) sampling is introduced and analyzed in detail, showing that the trivial necessary condition for its existence is actually sufficient. Some examples are…

In this paper branching rules for the fundamental representations of the symplectic groups in positive characteristic are found. The submodule structure of the restrictions of the fundamental modules for the group $Sp_{2n}(K)$ to the…

We study, for the first time, the maximum modulus set of a quasiregular map. It is easy to see that these sets are necessarily closed, and contain at least one point of each modulus. Blumenthal showed that for entire maps these sets are…

We begin with recalling the correspond theorem of induced modules and global sections of vector bundles. After that, we give a generalization of this theorem. Finally, we apply the result to branching laws, and give some concrete examples.

A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…

The blow-up lemma states that a system of super-regular pairs contains all bounded degree spanning graphs as subgraphs that embed into a corresponding system of complete pairs. This lemma has far-reaching applications in extremal…

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…

Over some types of trees with a given number of vertices, which trees minimize or maximize the total number of subtrees or leaf containing subtrees are studied. Here are some of the main results:\ (1)\, Sharp upper bound on the total number…

A concept of a rectangular diagram of a foliation in the three-sphere is introduced. It is shown that any co-orientable finite depth foliation in the complement of a link admits a presentation by a rectangular diagram compatible with the…

We aim to construct an element satisfying Hemmer's combinatorial criterion for $H^1(\mathfrak{S}_n, S^\lambda)$ to be non-vanishing. In the process, we discover an unexpected and surprising link between the combinatorial theory of integral…

Using methods from random matrix theory researchers have recently calculated the full spectra of random networks with arbitrary degrees and with community structure. Both reveal interesting spectral features, including deviations from the…