Related papers: Some examples of universal and generic partial ord…
We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite…
For an arbitrary partially ordered set $P$ its {\em dual} $P^*$ is built as the collection of all monotone mappings $P\to\2$ where $\2=\{0,1\}$ with $0<1$. The set of mappings $P^*$ is proved to be a complete lattice with respect to the…
We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…
Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…
Order and symmetry are main structural principles in mathematics. We give five examples where on the face of it order is not apparent, but deeper investigations reveal that they are governed by order structures. These examples are finite…
In this paper, we extend the notion of orthogonality to the general elements of an absolute matrix order unit space and relate it to the orthogonality among positive elements. We introduce the notion of a partial isometry in an absolute…
We introduce a partial order structure on the set of interval orders of a given size, and prove that such a structure is in fact a lattice. We also provide a way to compute meet and join inside this lattice. Finally, we show that, if we…
In this paper, we give some generalizations the concept of element order and we study some of the properties of these generalized order. In particular, with using this generalization we derive two solvability criteria.
We propose a notion of a generalized order, which can be used for the notion of a strict partial order. We introduce a weak order to replace the usual weak order defined from a strict partial order. In a constructive setting, that usual…
This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
A family of partial orders in the free monoid of words, induced from a partial order in alphabet, is presented. The induced orders generalize the chronological posets that have been defined for the two-letter alphabet only, and the…
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…
The set of finite words over a well-quasi-ordered set is itself well-quasi-ordered. This seminal result by Higman is a cornerstone of the theory of well-quasi-orderings and has found numerous applications in computer science. However, this…
Some partial orderings which compare probability distributions with the expo- nential distribution, are found to be very useful to understand the phenomenon of ageing. Here, we introduce some new generalized partial orderings which de-…
We investigate the set of partial partitions of a finite set, ordered by inclusion. With this ordering the set of partial partitions can be studied as an abstract simplicial complex. We use the theory of shellable nonpure complexes to find…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…
A duality between general partially ordered sets and certain topolgical spaces with two closures is established.
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…