Compact Representations of Ordered Sets

co.combinatorics - Open questions about posets - MathOverflow

Partially ordered sets (posets) are important objects in combinatorics (with basic connections to extremal combinatorics and to algebraic combinatorics)

Topology on Semi-Well Ordered Sets

A well ordered set with order topology is compact if and only if it has the greatest element. But a semi-well-ordered set need not be compact, ...

How can an ordered pair be expressed as a set?

Sets don't preserve order, but ordered pairs do. How does the ... Poor ∅ has been neglected, an easy thing to do, since it is so small.

Continuous functions on countable compact ordered sets as sums of ...

Every continuous function from a countable compact linearly ordered set A into a Banach space V (vanishing at the least element of A) admits a representation ...

Small Representations of Permutation Groups by Embedding the ...

We present a representation for permutation groups as the automorphism group of an ordered set \(U\) such that the automorphism group's action on a subset ...

Order theory - Wikipedia

2.1 Partially ordered sets · 2.2 Visualizing a poset · 2.3 Special elements within an order · 2.4 Duality · 2.5 Constructing new orders.

Some Representation Theorems for Partially Ordered Sets - jstor

A disjunctive partially ordered set P in which each maximal dual ideal is prime is isomorphic to a basis for the closed sets of a compact Ti-space. PROOF ...

some representation theorems for partially ordered sets

Semantic Scholar extracted view of "SOME REPRESENTATION THEOREMS FOR PARTIALLY ORDERED SETS" by E. S. Wölk.

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What Comes After Interval Orders? - Lehigh University

▷ Another motivation - compact representations of ordered sets. ▷ Example above - ground set is weak orders. Question: what if in addition bounds are ...

The dimension of random ordered sets - ACM Digital Library

Recommendations · Dynamic ordered sets with exponential search trees · Compact representations of ordered sets · Ordered and unordered top-K range reporting in ...

Topology on Semi-Well Ordered Sets

In this representation A is the set consisting of all elements of X with ... Compact semi-well ordered sets are characterised by the following theorem ...

Partially Ordered Sets (Chapter 3) - Enumerative Combinatorics

Partially Ordered Sets · Stably compact spaces and compact pospaces · Matchings and Radon transforms in lattices II. Concordant sets · A sheaf representation and ...

Compact representations of search in complex domains ...

The generalization is from searching over totally ordered sets to searching over more complex search domains such as trees, partial orders and general set ...

Field-independent representations of partially ordered sets

Article Field-independent representations of partially ordered sets was published on January 1, 1992 in the journal Forum Mathematicum ...

Well-ordered set with greatest element is compact

Let X be a well-ordered set with a greatest element α. We consider all sets of the form ]x,y] where y∈X and x is either another element of X or the symbol ←.

Partially ordered set - Encyclopedia of Mathematics

Every partially ordered set P can be considered as a small category, whose objects are the elements of P and in which the set of morphisms H(a,b) ...

Compact Representations Of Search In Complex Domains

Intuitively, this search game is a mathematical generalization of the well known binary search. The generalization is from searching over totally ordered sets ...

COMPACT REPRESENTATIONS OF SEARCH IN COMPLEX ...

Intuitively, this search game is a mathematical generalization of the well known binary search. The generalization is from searching over totally ordered sets ...

Learning with Partially Ordered Representations - ACL Anthology

Observe that (Subfact(M,w),v) is a partially ordered set (poset). The next ... However, we are primarily interested in the case when Subfactk(D) are a small ...