Related papers: Basic Orders for Defect Two Blocks of $\Z_p\Sym_n$

Linear second order recursive sequences with arbitrary initial conditions are studied. For sequences with the same parameters a ring and a group is attached, and isomorphisms and homomorphisms are established for related parameters. In the…

We pursue the question how integers can be ordered or partitioned according to their divisibility properties. Based on pseudometrics on $\mathbb{Z}$, we investigate induced preorders, associated equivalence relations, and quotient sets. The…

We show that double cosets of the infinite symmetric group with respect to some special subgroups admit natural structures of semigroups. We interpret elements of such semigroups in combinatorial terms (chips, colored graphs,…

We describe a straightforward construction of the pseudo-split absolutely pseudo-simple groups of minimal type with irreducible root systems of type $BC_n$; these exist only in characteristic $2$. We also give a formula for the dimensions…

We consider $2$-blocks of finite groups with defect group $D=Q \times R$ and inertial quotient $\mathbb{E}$ where $Q \cong (C_{2^m})^n$, $R \cong C_{2^r}$, and $\mathbb{E}$ contains a Singer cycle of $\operatorname{Aut}(Q)$ (an element of…

The simplicial endofunctor induced by a comonad in some category may underly a cyclic object in its category of endofunctors. The cyclic symmetry is then given by a sequence of natural transformations. We write down the commutation…

We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…

We determine the numerical invariants of blocks with defect group D_{2^n}\times C_{2^m}, where D_{2^n} denotes a dihedral group of order 2^n and C_{2^m} denotes a cyclic group of order 2^m. This generalizes Brauer's results for m=0. As a…

In this note, we construct a 2-basic set of the alternating group \A_n. To do this, we construct a 2-basic set of the symmetric group \sym_n with an additional property, such that its restriction to \A_n is a 2-basic set. We adapt here a…

Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…

Let B be a p-block of the finite group G. We observe that the p-fusion of G constrains the module structure of B: Any basis of B that is invariant under the left and right multiplications of a chosen Sylow p-subgroup S of G must in fact…

We consider the set Bp of parametric block correlation matrices with p blocks of various (and possibly different) sizes, whose diagonal blocks are compound symmetry (CS) correlation matrices and off-diagonal blocks are constant matrices.…

In this short note, we show some inequalities on Cartan matrices, centers and socles of blocks of group algebras. Our main theorems are generalizations of the facts on dimension of Reynolds ideals.

An n \times n matrix A has a normal defect of k if there exists an (n+k) \times (n+k) normal matrix A_{ext} with A as a leading principal submatrix and k minimal. In this paper we compute the normal defect of a special class of 4 \times 4…

The groups which can act semisymmetrically on a cubic graph of twice odd order are determined modulo a normal subgroup which acts semiregularly on the vertices of the graph.

We determine the mean number of 2-torsion elements in class groups of cubic orders, when such orders are enumerated by discriminant. Specifically, we prove that when isomorphism classes of totally real (resp., complex) cubic orders are…

We give a short and purely bilinear proof of the fact that two chains of $p$-elementary lattices with quadratic form or alternating bilinear form over the $p$-adic integers ore more generally over a complete discrete valuation ring have…

We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a combinatorial construction (blocker duality) which yields…

We settle the existence of certain "anti-magic" cubes using combinatorial block designs and graph decompositions to align a handful of small examples.

We show that the subgroup of the Picard group of a $p$-block of a finite group given by bimodules with endopermutation sources modulo the automorphism group of a source algebra is determined locally in terms of the fusion system on a defect…