Related papers: Well quasi-order and atomicity for combinatorial s…
In this article, we study "questionable representations" of (partial or total) orders, introduced in our previous article "A class of orders with linear? time sorting algorithm". (Later, we consider arbitrary binary functional/relational…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
We classify finite posets with a particular sorting property, generalizing a result for rectangular arrays. Each poset is covered by two sets of disjoint saturated chains such that, for any original labeling, after sorting the labels along…
An arrangement of pseudocircles is a finite set of oriented closed Jordan curves each two of which cross each other in exactly two points. To describe the combinatorial structure of arrangements on closed orientable surfaces, in (Linhart,…
Patterns of avoidance, adjacency, and association in complex systems design emerge from the system's underlying logical architecture (functional relationships among components) and physical architecture (component physical properties and…
Well-structured systems, aka WSTSs, are computational models where the set of possible configurations is equipped with a well-quasi-ordering which is compatible with the transition relation between configurations. This structure supports…
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 extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and…
Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space.…
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…
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…
In "Bipartite minors" [Journal of Combinatorial Theory, Series B, 2016], Chudnovsky et al. introduced the bipartite minor relation, a quasi-order on the class of bipartite graphs somewhat analogous the minor relation on general graphs and…
A relational structure is called reversible iff every bijective endomorphism of that structure is an automorphism. We give several equivalents of that property in the class of disconnected binary structures and some its subclasses. For…
The cumulative hierarchy conception of set, which is based on the conception that sets are inductively generated from "former" sets, is generally considered a good way to create a set conception that seems safe from contradictions. This…
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…
With this work we aim to show how Mathematica can be a useful tool to investigate properties of combinatorial structures. Specifically, we will face enumeration problems on independent subsets of powers of paths and cycles, trying to…
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…
Dlab and Ringel showed that algebras being quasi-hereditary in all total orders for indices of primitive idempotents becomes hereditary. So, we are interested in for which orders a given quasi-hereditary algebra is again quasi-hereditary.…
In the development of operational semantics of concurrent systems, a key decision concerns the adoption of a suitable notion of execution model, which basically amounts to choosing a class of partial orders according to which events are…
This paper is devoted to characterizing the so-called order isomorphisms intertwining the $L^2$-semigroups of two Dirichlet forms. We first show that every unitary order isomorphism intertwining semigroups is the composition of…