A tree-composition is a tree-like family that serves to describe the obstacles to k-edge-connected orientability of mixed graphs. Here we derive a structural result on tree-compositions that gives rise to a simple algorithm for computing an obstacle when the orientation does not exist. As another application, we show a min–max theorem on the minimal in-degree of a given node set in a k-edge-con...

Noting that the usual ‘propositionally’ based way of composing retrenchments can yield many ‘junk’ cases, alternative approaches to composition are introduced (via notions of tidy, neat, and fastidious retrenchments) that behave better in this regard. These alternatives do however make other issues such as associativity harder. The technical details are presented for vertical composition of ret...

Health saving is the main state program and a priority direction of scientific centers in Russia Kuzbass. One most important tasks transformation agricultural raw materials on basis new technological solutions for creation food products with desired functional properties. Its solution connected basics physicochemical, biochemical processes production dairy protein increased biological value imm...

Given integers a1, a2, . . . , an, with a1 + a2 + · · ·+ an ≥ 1, a symmetrically constrained composition λ1 + λ2 + · · ·+ λn =M of M into n nonnegative parts is one that satisfies each of the the n! constraints {∑n i=1 aiλπ(i) ≥ 0 : π ∈ Sn } . We show how to compute the generating function of these compositions, combining methods from partition theory, permutation statistics, and lattice-point ...

We study formulas for Fibonacci numbers as sums over compositions. The Fibonacci number Fn+1 is the number of compositions of n with parts 1 and 2. Compositions with parts 1 and 2 form a free monoid under concatenation, and our formulas arise from free submonoids of this free monoid.

Feature modeling is a popular domain analysis method for describing the commonality and variability among the domain products. The current formalisms of feature modelling do not have enough support for automated domain product configuration and validation. We have developed a theory of feature modeling: a feature model is analogous to a definition of a language; a particular feature composition...

In this paper we introduce a new graph composition, called 2-amalgam, and we prove that the 2-amalgam of perfect graphs is perfect. This composition generalizes many of the operations known to preserve perfection, such as the clique identification, substitution, join and amalgam operations. We give polynominal-time algorithms to determined whether a general graph is decomposable with respect to...

In this paper we consider the absolute variation statistics of a composition σ = σ1 · · ·σm of n which is a measure of the sum of absolute differences between each consecutive pair of parts in a composition. This and some related statistics which we discuss, can also be interpreted within the context of bargraph polygons and bargraph walks of area n. In this context, absolute variation correspo...

A (1, k)-composition of a positive integer n consists of an ordered sequence of the integers 1 and k whose sum is n. A palindromic (1, k)-composition is one for which the sequence is the same from left to right as from right to left. We give recursive equations and generating functions for the total number of such compositions and palindromes, and for the number of 1’s, k’s, “+”signs and summan...