Related papers: Representable posets
A quotient of a poset $P$ is a partial order obtained on the equivalence classes of an equivalence relation $\theta$ on $P$; $\theta$ is then called a congruence if it satisfies certain conditions, which vary according to different…
A careful study is made of embeddings of posets which have a convex range. We observe that such embeddings share nice properties with the homomorphisms of more restrictive categories; for example, we show that every order embedding between…
A set $\mathcal{A}$ is said to be an additive $h$-basis if each element in $\{0,1,\ldots,hn\}$ can be written as an $h$-sum of elements of $\mathcal{A}$ in {\it at least} one way. We seek multiple representations as $h$-sums, and, in this…
In this paper we introduce and study the poset of equivalence classes of subgroups of a finite group $G$, induced by the isomorphism relation. This contains the well-known lattice of solitary subgroups of $G$. We prove that in several…
We study some properties of the coset poset associated with the family of subgroups of class $\leq 2$ of a nilpotent group of class $\leq 3$. We prove that under certain assumptions on the group the coset poset is simply-connected if and…
A poset ${\mathbb{P}}$ is called reversible iff every bijective homomorphism $f:{\mathbb{P}} \rightarrow {\mathbb{P}}$ is an automorphism. Let ${\mathcal{W}}$ and ${\mathcal{W}} ^*$ denote the classes of well orders and their inverses…
This paper provides a general characterization of preferences that admit a Richter-Peleg representation without imposing completeness or transitivity. We establish that a binary relation on a nonempty set admits a Richter-Peleg…
We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…
We establish formulas for the number of all downsets (or equivalently, of all antichains) of a finite poset P. Then, using these numbers, we determine recursively and explicitly the number of all posets having a fixed set of minimal points…
A poset is called upper homogeneous, or "upho," if every principal order filter of the poset is isomorphic to the whole poset. We study (finite type $\mathbb{N}$-graded) upho lattices, with an eye towards their classification. Any upho…
We study computably enumerable equivalence relations (abbreviated as ceers) under computable reducibility, and we investigate the resulting degree structure Ceers, which is a poset with a smallest and a greatest element. We point out a…
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…
This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then…
In this talk we discuss the relations between representations of algebraic groups and principal bundles on algebraic varieties, especially in characteristic $p$. We quickly review the notions of stable and semistable vector bundles and…
We extend the notion of representation of a matroid to algebraic structures that we call skew partial fields. Our definition of such representations extends Tutte's definition, using chain groups. We show how such representations behave…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
We consider the problem of determining whether a set of primes, or, more generally, prime ideals in a number field, can be realized as a finite union of residue classes, or of Frobenius conjugacy classes. We give criteria for a set to be…
We show that the separative quotient of the poset (P(L),\subset) of isomorphic suborders of a countable scattered linear order L is \sigma-closed and atomless. So, under the CH, all these posets are forcing-equivalent (to P(\omega)/Fin).
We explore representing the compact subsets of a given represented space by infinite sequences over Plotkin's $\mathbb{T}$. We show that computably compact computable metric spaces admit representations of their compact subsets in such a…
When a linear order has an order preserving surjection onto each of its suborders we say that it is strongly surjective. We prove that the set of countable strongly surjective linear orders is complete for the class of sets which are the…