Related papers: Symmetric group blocks of small defect

We report some group divisible designs with block size five, including types $6^{15}$ and $10^{15}$. As a consequence we are able to extend the known spectrum for 5-GDDs of type $g^u$.

Computational techniques for the construction of quasi-symmetric block designs are explored and applied to the case with $56$ points. One new $(56,16,18)$ and many new $(56,16,6)$ designs are discovered, and non-existence of $(56,12,9)$ and…

This work focuses on non-adaptive combinatorial group testing, with a primary goal of efficiently identifying a set of at most $d$ defective elements among a given set of $n$ elements using the fewest possible tests. Non-adaptive…

To each pair consisting of a saturated fusion system over a $p$-group together with a compatible family of K\"ulshammer-Puig cohomology classes, one can count weights in a hypothetical block algebra arising from these data. When the pair…

We consider the existence problem for a semi-cyclic holey group divisible design of type (n,m^t) with block size 3, which is denoted by a 3-SCHGDD of type (n,m^t). When t is odd and n\neq 8 or t is doubly even and t\neq 8, the existence…

Using the classification of finite simple groups we prove Alperin's weight conjecture and the character theoretic version of Broue's abelian defect group conjecture for 2-blocks of finite groups with an elementary abelian defect group of…

The band-unfolding method is widely used to calculate the effective band structures of a disordered system from its supercell model. The unfolded band structures show the crystallographic symmetry of the underlying structure, where the…

In this paper we will consider the 2-fold symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2pi/p with p no smaller than 2. We will mainly concentrate on the groups where some elements are…

We prove a conjecture by Belmans, Fu and Krug concerning the Hochschild homology of the symmetric powers of a small dg category $\mathscr{C}$. More precisely, we show that these groups decompose into pieces that only depend on the…

The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite groups. We also compare the classical, exterior and symmetric…

The tensor rank decomposition is a useful tool for the geometric interpretation of the tensors in the canonical tensor model (CTM) of quantum gravity. In order to understand the stability of this interpretation, it is important to be able…

We study a weakened version of the Holm--Willems Local Conjecture. The problem is reduced to quasi-simple groups under the assumption that the defect group is abelian. Complete proofs are provided in the case \(p = 2\).

For any prime p, we construct, and simultaneously count, all of the complex Specht modules in a given p-block of the symmetric group which remain irreducible when reduced modulo p. We call the Specht modules with this property p-irreducible…

This paper investigates the critical group of a faithful representation of a finite group. It computes the order of the critical group in terms of the character values, and gives some restrictions on its subgroup structure. It also computes…

We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…

A Space-Time Block Code (STBC) in $K$ symbols (variables) is called $g$-group decodable STBC if its maximum-likelihood decoding metric can be written as a sum of $g$ terms such that each term is a function of a subset of the $K$ variables…

In this paper we study how certain symmetries of convex bodies affect their geometric properties. In particular, we consider the impact of symmetries generated by the block diagonal subgroup of orthogonal transformations, generalizing…

We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric…

We introduce polyhedral cones associated with $m$-hemimetrics on $n$ points, and, in particular, with $m$-hemimetrics coming from partitions of an $n$-set into $m+1$ blocks. We compute generators and facets of the cones for small values of…

We develop an elementary algebraic method to compute the center of the principal block of a small quantum group associated with a complex semisimple Lie algebra at a root of unity. The exemplary case of $\mathfrak{sl}_3$ is computed…