Related papers: Some examples of universal and generic partial ord…
Chen, Kitaev, M\"{u}tze, and Sun recently introduced the notion of universal partial words, a generalization of universal words and de Bruijn sequences. Universal partial words allow for a wild-card character $\diamond$, which is a…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
Every reduced ring $R$ has a natural partial order defined by $a\le b$ if $a^2=ab$; it generalizes the natural order on a boolean ring. The article examines when $R$ is a lower semi-lattice in this order with examples drawn from weakly Baer…
We show that the category of partially ordered sets $\mathsf{Pos}$ is equivalent to the free conservative cocompletion of the category of finite non-empty totally ordered sets $\Delta$, which is also known as the simplex category.
Orthogonal surfaces are nice mathematical objects which have interesting connections to various fields, e.g., integer programming, monomial ideals and order dimension. While orthogonal surfaces in one or two dimensions are rather trivial…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving…
We study a type of object, called a pathway (generalizing pathways in the sense of P. E. Cohen [Proc. Amer. Math. Soc. 74, No. 2 (1979), 318--321]), which is useful for several set-theoretic constructions and whose existence, in a sense,…
We define what is meant by a strict total order in a category having subobjects, products and fibre products. This allows us to define the notions of an ordered bundle X and an ordered G-set; when G=\pi_1(X) we relate these structures to…
When we work with information from multiple sources, the formalism each employs to handle uncertainty may not be uniform. In order to be able to combine these knowledge bases of different formats, we need to first establish a common basis…
Compositional generalization is the ability to generalize systematically to a new data distribution by combining known components. Although humans seem to have a great ability to generalize compositionally, state-of-the-art neural models…
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
Word order is an important concept in natural language, and in this work, we study how word order affects the induction of world knowledge from raw text using language models. We use word analogies to probe for such knowledge. Specifically,…
Dilatations modify categories by imposing that some morphisms factorize through some others. This is formalized by a universal property. This text is devoted to introduce and study this construction. Examples of dilatations of categories…
The elements of a finite nonempty partially ordered set are exposed at independent uniform times in $[0,1]$ to a selector who, at any given time, can see the structure of the induced partial order on the exposed elements. The selector's…
We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…
Override and update are natural constructions for combining partial functions, which arise in various program specification contexts. We use an unexpected connection with combinatorial geometry to provide a complete finite system of…
We summarize some facts on chains (totally ordered sets), from an order-theoretic and from a topological point of view. We highlight the fact that many classical theorems that are true for partially ordered sets under some completeness…
We provide a classification of the homogeneous 3-dimensional permutation structures, i.e. homogeneous structures in a language of 3 linear orders, partially answering a question of Cameron. We also arrive at a natural description of all…