Related papers: Partially ordered sets in Macaulay2
In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multivariate polynomials, and only a small…
A "partial ordering" is a way to heuristically order a set of examples (partial orderings are a set where, for certain pairs of elements, one precedes the other). While these orderings may only be approximate, they can be useful for guiding…
We introduce the package combinatorics for the software CoCoA. This package provides a data structure and the necessary methods for computing several known enumerative combinatorial invariants.
Coxeter polynomials are important homological invariants that are defined for a large class of finite-dimensional algebras. It is of particular interest to develop methods to compute these polynomials. We define the notion of insertion of a…
The main purpose of this article is to pose three problems which are easy to be formulated in an elementary way. These problems which are specifically important also for the new class of partially ordered sets seem to be not yet solved.
We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains.
In order to be able to use methods of Universal Algebra for investigating posets, we assign to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset a certain algebra…
The W-set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. We explicitly describe in a purely combinatorial manner the W-sets of the weak order…
Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant…
We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested…
A chain poset, by definition, consists of chains of ordered elements in a poset. We study the chain posets associated to two posets: the Boolean algebra and the poset of isotropic flags. We prove that, in both cases, the chain posets…
A supplemental paper detailing the QuillenSuslin package for Macaulay2. The QuillenSuslin package for Macaulay2 provides the ability to compute a free basis for a projective module over a polynomial ring with coefficients in Q, Z or Z/p for…
We generate and count isomorphism classes of gluing-parallel posets with interfaces (iposets) on up to eight points, and on up to ten points with interfaces removed. In order to do so, we introduce a new class of iposets with full…
Partial orders may be used for modeling and summarising ranking data when the underlying order relations are less strict than a total order. They are a natural choice when the data are lists recording individuals' positions in queues in…
The Interval poset of a permutation is an effective way of capturing all the intervals of the permutation and the inclusions between them and was introduced recently by Tenner. Thi paper explores the geometric interpretation of interval…
Motivated by the study of the recurrent orbits in a Morse set of a Morse decomposition, we introduce the concept of Morse predecomposition of an isolated invariant set in the setting of combinatorial and classical dynamical systems. We…
We introduce two partially ordered sets, $P^A_n$ and $P^B_n$, of the same cardinalities as the type-A and type-B noncrossing partition lattices. The ground sets of $P^A_n$ and $P^B_n$ are subsets of the symmetric and the hyperoctahedral…
We describe an ACL2 package for defining partial recursive functions that also supports efficient execution. While packages for defining partial recursive functions already exist for other theorem provers, they often require inductive…
This is the Hadamard package for Macaulay2 which computes the Hadamard product of projective subvarieties.
Choreographies describe possible sequences of interactions among a set of agents. We aim to join two lines of research on choreographies: the use of the shuffle on trajectories operator to design more expressive choreographic languages, and…