Related papers: A Note on Invariant Extensions of Preorders
In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…
We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on $n$ elements,…
Nontransitive choices have long been an area of curiosity within economics. However, determining whether nontransitive choices represent an individual's preference is a difficult task since choice data is inherently stochastic. This paper…
This paper explores a new class of incomplete preferences -- termed ``connected preferences'' -- in which maximal domains of comparability are topologically connected. We provide necessary and sufficient conditions for continuous…
Our paper deals with the investigation of extensions of commutative groups by loops so that the quasigroups that result in the multiplication between cosets of the kernel subgroup are T-quasigroups. We limit our study to extensions in which…
The finite satisfiability problem for the two-variable fragment of first-order logic interpreted over trees was recently shown to be ExpSpace-complete. We consider two extensions of this logic. We show that adding either additional binary…
Consider a linear ordering equipped with a finite sequence of monadic predicates. If the ordering contains an interval of order type \omega or -\omega, and the monadic second-order theory of the combined structure is decidable, there exists…
Quandle cocycles are constructed from extensions of quandles. The theory is parallel to that of group cohomology and group extensions. An interpretation of quandle cocycle invariants as obstructions to extending knot colorings is given, and…
Some general properties of abstract relations are closely examined. These include generalizations of linearity, and properties based on `pinning' an inequality by a pair of families of endomorphisms.To each property we try to associate a…
The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…
It is well-known that constructing models of higher-order probabilistic programming languages is challenging. We show how to construct step-indexed logical relations for a probabilistic extension of a higher-order programming language with…
We study the existence of stable matchings when agents have choice correspondences instead of preference relations. We extend the framework of \cite{chambers2017choice} by weakening the path independence assumption. For many-to-many…
Given a linearly ordered set I, every surjective map p: A --> I endows the set A with a structure of set of preferences by "replacing" the elements of I with their inverse images via p considered as "balloons" (sets endowed with an…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize all hypersubstitutions which provide bijections on the set of all terms. The set of all such hypersubstitutions forms a monoid.…
We introduce the concept of braided noncommutative Poisson bialgebras. The theory of cocycle bicrossproducts for noncommutative Poisson bialgebras is developed. As an application, we solve the extending problem by using some non-abelian…
Let $(P,\leq)$ be a finite poset (partially ordered set), where $P$ has cardinality $n$. Consider linear extensions of $P$ as permutations $x_1x_2\cdots x_n$ in one-line notation. For distinct elements $x,y\in P$, we define…
We study the classical invariant theory of the Bezoutiant R(A,B) of a pair of binary forms A,B. It is shown that R(A,B) admits a Taylor expansion whose coefficients are (essentially) the odd transvectants (A,B)_{2r+1}. Moreover, R(A,B) is…
In this paper we study possibilities of efficient reasoning in combinations of theories over possibly non-disjoint signatures. We first present a class of theory extensions (called local extensions) in which hierarchical reasoning is…
We study problems related to indecomposability of modules over certain local finite dimensional trivial extension algebras. We do this by purely combinatorial methods. We introduce the concepts of graph of cyclic modules, of combinatorial…