We study the unitary Cayley graph associated to an arbitrary finite ring, determining precisely its diameter, girth, eigenvalues, vertex and edge connectivity, and vertex and edge chromatic number. We also compute its automorphism group, settling a question of Klotz and Sander. In addition, we classify all planar graphs and perfect graphs within this class.

A linear (qd, q, t)-perfect hash family of size s in a vector space V of order qd over a field F of order q consists of a set φ1, . . . , φs of linear functionals from V to F with the following property: for all t subsets X ⊆ V there exists i ∈ {1, . . . , s} such that φi is injective when restricted to F . A linear (qd, q, t)-perfect hash family of minimal size d(t− 1) is said to be optimal. I...

Let h be a connective homology theory. We construct functorial relative plus construction as Bousfield localization functor in the category of maps spaces. It allows us to associate pair (X,H), consisting connected space X and an h-perfect normal subgroup H fundamental group π1(X), h-acyclic map X→XH+h inducing quotient by on group. show that this is terminal among kill H. When ordinary theory ...

Super-simple designs are useful in constructing codes and designs such as superimposed codes and perfect hash families. Recently, Gronau et al determined the existence of super-simple (v, 5, 2)-BIBDs with possible exceptions of v ∈ {75, 95, 115, 135, 195, 215, 231, 285, 365, 385, 515}. In this article, we investigate the existence of a super-simple (v, 5, 4)-BIBD and show that such a design exi...

We present two new perfect hashing schemes that can be used for efficient bitboard move generation for sliding pieces in chess-like board games without the need to use rotated bitboards. Moreover, we show that simple variations of these schemes give minimal perfect hashing schemes. The new method is applicable provided N , the number of k-bit spaced positions that may be set to 1, is not more t...

We classify 1-tilting classes over an arbitrary commutative ring. As a consequence, we classify all resolving subcategories of finitely presented modules of projective dimension at most 1. Both these collections are in 1-1 correspondence with faithful Gabriel topologies of finite type, or equivalently, with Thomason subsets of the spectrum avoiding a set of primes associated in a specific way t...

Denef and Loeser defined a map from the Grothendieck ring of sets definable in pseudo-finite fields to the Grothendieck ring of Chow motives, thus enabling to apply any cohomological invariant to these sets. We generalize this to perfect, pseudo algebraically closed fields with pro-cyclic Galois group. In addition, we define some maps between different Grothendieck rings of definable sets which...

The title compound, C21H24FN2O2+.Cl-.C3H8O, is a potential drug designed as a hybrid compound with antihypertensive, antioxidant and beta-adrenolytic activity. The cation contains nearly planar benzofuran and fluorophenyl ring systems, as well as a piperazine ring adopting an almost perfect chair conformation. The benzofuran and piperazine moieties are connected by an ethyl chain, the moieties ...

We determine exactly which formal deformation functors of representations of a finite group as weakly ramified automorphisms of a power series ring over a perfect field of positive characteristic are prorepresentable: only in characteristic two, the weak action of an involution and of the Klein group have non-pro-representable mixedcharacteristic formal deformation functors, and only the first ...