The digit-recurrence division relies on a sequence of addition/subtraction and shift operations in a manner similar to the paper-and-pencil approach, that gives a very regular structure suitable for efficient VLSI implementation. Speed is obtained through the use of redundant number notation allowing carry-propagation-free addition/subtraction with a delay independent of the size of the divisor...

In [M. Klin, A. Munemusa, M. Muzychuk, P.-H. Zieschang Directed strongly regular graphs obtained from coherent algebras. Linear Algebra and its Applications 337, (2004) 83-109] the flag algebra of a given balanced incomplete block design with parameters (ν, b, r, k, λ) where λ = 1, has been constructed. In this paper, we consider the association scheme which is related to this flag algebra. By ...

We present the results of an investigation into the representations of Archimedean polyhedra (those polyhedra containing only one type of vertex gure) as quotients of regular abstract polytopes. Two methods of generating these presentations are discussed, one of which may be applied in a general setting, and another which makes use of a regular polytope with the same automorphism group as the d...

We introduce some constructions of weakly distance-regular digraphs of girth 2, and prove that a certain quotient digraph of a commutative weakly distance-transitive digraph of girth 2 is a distancetransitive graph. As an application of the result, we obtain some examples of weakly distanceregular digraphs which are not weakly distance-transitive. Moreover, a class of commutative weakly distanc...

We formalize a unified framework for verified decision procedures for regular expression equivalence. Five recently published formalizations of such decision procedures (three based on derivatives, two on marked regular expressions) can be obtained as instances of the framework. We discover that the two approaches based on marked regular expressions, which were previously thought to be the same...

Let G be a non-bipartite strongly regular graph on n vertices of valency k. We prove that if G has a distance-regular antipodal cover of diameter 4, then k ≤ 2(n + 1)/5 , unless G is the complement of triangular graph T (7), the folded Johnson graph J (8, 4) or the folded halved 8-cube. However, for these three graphs the bound k ≤ (n − 1)/2 holds. This result implies that only one of a complem...

The paper studies some variants of deletion operations which generalize the left/right quotient of languages. The main emphasis is put on how these deletions can be expressed as a combination of other operations, and on closure properties of various language families under deletion. Some results are the expected ones: the sequential (iterated sequential, dipolar) deletion from a regular languag...

A lift of a given network is a network that admits the first network as quotient. Assuming that a bifurcation occurs for a coupled cell system consistent with the structure of a regular network (in which all cells have the same type and receive the same number of inputs and all arrows have the same type), it is well known that some lifts exhibit new bifurcating branches of solutions. In this wo...

This paper studies the homological determinants and Nakayama automorphisms of not-necessarily-noetherian m-Koszul twisted Calabi-Yau or, equivalently, m-Koszul Artin-Schelter regular, algebras. Dubois-Violette showed that such an algebra is isomorphic to a derivation quotient algebra D(w, i) for a unique-up-to-scalar-multiples twisted superpotential w. By definition, D(w, i) is the quotient of ...