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pro vyhledávání: '"05E18"'
In this paper, we introduce orbit matrices of directed strongly regular graphs (DSRGs). Further, we propose a method of constructing directed strongly regular graphs with prescribed automorphism group using genetic algorithm. In the construction, we
Externí odkaz:
http://arxiv.org/abs/2412.14787
Motivated by recent interest to $F$-inverse monoids, on the one hand, and to restriction and birestriction monoids, on the other hand, we initiate the study of $F$-birestriction monoids as algebraic structures in the enriched signature $(\cdot, \, ^*
Externí odkaz:
http://arxiv.org/abs/2412.12082
Autor:
Maksimović, Marija, Rukavina, Sanja
In this paper we present a method for constructing directed strongly regular graphs with assumed action of an automorphism group. The application of this method leads to first examples of directed strongly regular graphs with parameters $(22,9,6,3,4)
Externí odkaz:
http://arxiv.org/abs/2412.10901
Autor:
Clarke, Oliver, Kölbl, Max
We study the hypersimplex under the action of the symmetric group $S_n$ by coordinate permutation. We prove that the evaluation of its equivariant $H^*$-polynomial at $1$ is the permutation character of decorated ordered set partitions under the natu
Externí odkaz:
http://arxiv.org/abs/2412.06524
Autor:
Hawtin, Daniel R.
A code ${\mathcal C}$ is a subset of the vertex set of a Hamming graph $H(n,q)$, and ${\mathcal C}$ is $2$-neighbour-transitive if the automorphism group $G={\rm Aut}({\mathcal C})$ acts transitively on each of the sets ${\mathcal C}$, ${\mathcal C}_
Externí odkaz:
http://arxiv.org/abs/2411.08351
Autor:
Dobson, Ted, Robson, Gregory
Let $G$ be a group. The BCI problem asks whether two Haar graphs of $G$ are isomorphic if and only if they are isomorphic by an element of an explicit list of isomorphisms. We first generalize this problem in a natural way and give a theoretical way
Externí odkaz:
http://arxiv.org/abs/2411.07652
There is strong evidence for the belief that `almost all' finite semigroups, whether we consider multiplication operations on a fixed set or their isomorphism classes, are nilpotent of index 3 (3-nilpotent for short). The only known method for counti
Externí odkaz:
http://arxiv.org/abs/2411.00466
We examine bicoset digraphs and their natural properties from the point of view of symmetry. We then consider connected bicoset digraphs that are $X$-joins with collections of empty graphs, and show that their automorphism groups can be obtained from
Externí odkaz:
http://arxiv.org/abs/2409.11092
Autor:
Green, R. M., Xu, Tianyuan
Let $W$ be a simply laced Weyl group of finite type and rank $n$. If $W$ has type $E_7$, $E_8$, or $D_n$ for $n$ even, then the root system of $W$ has subsystems of type $nA_1$. This gives rise to an irreducible Macdonald representation of $W$ spanne
Externí odkaz:
http://arxiv.org/abs/2409.01948
Autor:
Uchiumi, Ryo, Yoshinaga, Masahiko
For given linear action of a finite group on a lattice and a positive integer q, we prove that the mod q permutation representation is a quasi-polynomial in q. Additionally, we establish several results that can be considered as mod q-analogues of re
Externí odkaz:
http://arxiv.org/abs/2409.01084