A Characterization of Ordered Sets and Lattices via Betweenness Relations

2004 ◽  
Vol 46 (3-4) ◽  
pp. 237-250 ◽  
Author(s):  
Nico Düvelmeyer ◽  
Walter Wenzel
Keyword(s):  
Ordered Sets ◽  
Betweenness Relations

scholarly journals A Combinatorial Approach for Small and Strong Formulations of Disjunctive Constraints

2019 ◽  
Vol 44 (3) ◽  
pp. 793-820 ◽  
Author(s):  
Joey Huchette ◽  
Juan Pablo Vielma
Keyword(s):  
Piecewise Linear ◽  
Expressive Power ◽  
Complete Characterization ◽  
Linear Functions ◽  
Mixed Integer ◽  
Ordered Sets ◽  
Special Ordered Sets ◽  
Disjunctive Constraints

A framework is presented for constructing strong mixed-integer programming formulations for logical disjunctive constraints. This approach is a generalization of the logarithmically sized formulations of Vielma and Nemhauser for special ordered sets of type 2 (SOS2) constraints, and a complete characterization of its expressive power is offered. The framework is applied to a variety of disjunctive constraints, producing novel small and strong formulations for outer approximations of multilinear terms, generalizations of special ordered sets, piecewise linear functions over a variety of domains, and obstacle avoidance constraints.

A Characterization of Partially Ordered Sets with Linear Discrepancy Equal to 2

Order ◽  
2007 ◽  
Vol 24 (3) ◽  
pp. 139-153 ◽  
Author(s):  
David M. Howard ◽  
Mitchel T. Keller ◽  
Stephen J. Young
Keyword(s):  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Linear Discrepancy ◽  
Partially Ordered

scholarly journals A characterization of finite Stone pseudocomplemented ordered sets

1996 ◽  
Vol 121 (2) ◽  
pp. 117-120
Author(s):  
Radomír Halaš
Keyword(s):  
Ordered Sets

Properties of m-ideals in partially ordered sets

2020 ◽  
pp. 601-606
Author(s):  
J. Catherine ◽  
B. Elavarasan
Keyword(s):  
Partially Ordered Sets ◽  
Prime Ideals ◽  
Ordered Sets ◽  
Partially Ordered

In this paper, we study the notion of $M$-ideals in partially ordered sets and examine the various properties of $M$-ideals. Further, the relations between $M$-ideals and $\alpha$-ideals in partially ordered sets are discussed. Moreover, a characterization of prime ideals to be $M$-ideals is obtained.

Decidability and finite axiomatizability of theories of ℵ0-categorical partially ordered sets

1981 ◽  
Vol 46 (1) ◽  
pp. 101-120 ◽  
Author(s):  
James H. Schmerl
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Finite Width ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Decidable Theory ◽  
Axiomatizable Theory ◽  
Finitely Axiomatizable Theory

AbstractEvery ℵ0-categorical partially ordered set of finite width has a finitely axiomatizable theory. Every ℵ0-categorical partially ordered set of finite weak width has a decidable theory. This last statement constitutes a major portion of the complete (with three exceptions) characterization of those finite partially ordered sets for which any ℵ0-categorical partially ordered set not embedding one of them has a decidable theory.

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