‎the number of factorizations of a finite abelian group as the product of two subgroups is computed in two different ways and a combinatorial identity involving gaussian binomial coefficients is presented‎.

An infinite family of T -factorizations of complete graphs K2n, where 2n = 56k and k is a positive integer, in which the set of vertices of T can be split into two subsets of the same cardinality such that degree sums of vertices in both subsets are not equal, is presented. The existence of such T -factorizations provides a negative answer to the problem posed by Kubesa.

Incomplete factorizations represent a class of algebraic preconditioners important from both theoretical and practical points of view. While state-of-the-art preconditioners of this kind can be very useful, very large problems, arising, e.g., from discretizations of complicated operators on unstructured grids typically, still may require more robust preconditioners. High-quality incomplete fact...

In this work we derive two families of radix-4 factorizations for the FFT (Fast Fourier Transform) that have the property that both inputs and outputs are addressed in natural order. These factorizations are obtained from another two families of radix-2 algorithms that have the same property. The radix-4 algorithms obtained have the same mathematical complexity (number of multiplications and ad...

A. Problems involving chains of irreducible factorizations in atomic integral domains and monoids have been the focus of much recent literature. If S is a commutative cancellative atomic monoid, then the catenary degree of S (denoted c(S )) and the tame degree of S (denoted t(S )) are combinatorial invariants of S which describe the behavior of chains of factorizations. In this note, we ...