The number of $n$-gaussoids is shown to be a double exponential function in $n$. necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing $3$-minors and encoding the resulting combinatorial constraints suitable transitive graph. Various special classes arise from restricting allowed $3$-minors.

We find the excluded minors for minor-closed class of lattice path polymatroids as a subclass Boolean polymatroids. Like matroids and polymatroids, there are infinitely many minors, but they fall into small number easily-described types.

The article considers the international experience of legal regulation labor minors and identifies promising areas for improving current legislation Ukraine in field work minors. In particular, authors studied Latvian, Lithuanian, Slovak, Estonian Republics, Great Britain, provinces Canada (Alberta Manitoba).
 As you know, has certain features both other countries, given their physiologica...

In this paper, we will show that the width of simplices defined by systems of linear inequalities can be computed in polynomial time if some minors of their constraint matrices are bounded. Additionally, we present some quasi-polynomial-time and polynomial-time algorithms to solve the integer linear optimization problem defined on simplices minus all their integer vertices assuming that some mi...

We consider the problem whether a permutation of a finite set is uniquely determined by its identification minors. While there exist non-reconstructible permutations of every set with two, three, or four elements, we show that every permutation of a finite set with at least five elements is reconstructible from its identification minors. Moreover, we provide an algorithm for recovering a permut...

We discuss the use of K-terminal networks to represent arbitrary clutters. A given clutter has many di¤erent representations, and there does not seem to be any set of simple transformations that can be used to transform one representation of a clutter into any other. We observe that for t 2 the class of clutters that can be represented using no more than t terminals is closed under minors, and ...