Results 271 to 280 of about 45,393 (304)

Endomorphisms of Partially Ordered Sets

Combinatorics, Probability and Computing, 1998
It is shown that every partially ordered set with n elements admits an endomorphism with an image of a size at least n1/7 but smaller than n. We also prove that there exists a partially ordered set with n elements such that each of its non-trivial endomorphisms has an image of size O((n log n)1/3).
Dwight Duffus, Tomasz Luczak 0001, Vojtech Rödl, Andrzej Rucinski 0001   +3 more
openaire   +3 more sources

Completions of Partially Ordered Sets

SIAM Journal on Computing, 1982
We show, for any subset system Z (as defined in Wright, Wagner, and Thatcher, T.C.S. 7 (1978), pp. 57–77) and any order preserving map $f:Q \to P$ of posets, the existence of a universal map $u_f :P \to P_f $ where $P_f $ is Z-complete and $u_f f$ is Z-continuous. This generalizes to arbitrary subset systems the result of Markowsky (T.C.S. 4 (1977), pp.
Bernhard Banaschewski, Evelyn Nelson
openaire   +1 more source

Splittability for Partially Ordered Sets

Order, 2000
This paper deals with an extension of the notion of splittability (cleavability) of topological spaces, introduced by Arkhangel'skij (1985), to partially ordered sets [\textit{D. J. Marron} and \textit{T. B. M. McMaster}, Math. Proc. R. Ir. Acad. 99A, 189-194 (1999; Zbl 0966.06002)] as follows: If \(A\) is a subset of a poset \(X\), we say that \(X ...
Alan J. Hanna, T. Brian M. McMaster
openaire   +1 more source

Decompositions of Partially Ordered Sets

Order, 2000
In a previous paper [J. Comb. Theory, Ser. A 89, 77-104 (2000; Zbl 0959.52010)] the authors characterized the cone of linear inequalities holding for the flag \(f\)-vectors of all graded posets of a given rank. In the paper under review they give a description of the cone of flag \(f\)-vectors of planar graded posets. The proof includes a special chain-
Louis J. Billera, Gábor Hetyei
openaire   +1 more source

Linear Inequalities for Flags in Graded Partially Ordered Sets

Journal of Combinatorial Theory - Series A, 2000
The closure of the convex cone generated by all flag f-vectors of graded partially ordered sets is shown to be polyhedral. In particular, we give the facet inequalities to the polar cone of all nonnegative chain-enumeration functionals on this class of ...
Louis J Billera, Gabor Hetyei
exaly   +2 more sources

Rough Sets in Partially Ordered Sets

2010 IEEE International Conference on Granular Computing, 2010
It is well-known to us that the Pawlak’s rough set theory, an effective tool to deal with uncertainty and granularity in information systems, is based on equivalence relation. However, in some situations, those conditions of equivalence relation are hardly met.
Kai Li, William Zhu 0001, Jianguo Tang
openaire   +1 more source

Partially ordered sets and stratification

Mathematical Social Sciences, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Raymond N. Greenwell, Tadeusz Krauze
openaire   +2 more sources

The Flow Set with Partial Order

Mathematics of Operations Research, 2008
The flow set with partial order is a mixed-integer set described by a budget on total flow and a partial order on the arcs that may carry positive flow. This set is a common substructure of resource allocation and scheduling problems with precedence constraints and robust network flow problems under demand/capacity uncertainty.
Alper Atamtürk, Muhong Zhang
openaire   +1 more source

Regulating Functions on Partially Ordered Sets

Order, 2005
Given a partially ordered set \((T,\leq)\) with the least element 0, the authors start with 3 functions \(\alpha,\beta,x:T\to R\), bounded on any interval \([0,t]\), \(t\in T\), and such that \(\alpha(0)\leq x(0)\leq\beta(0)\). They consider pairs \((l,u)\) of nonnegative, non-decreasing functions on \(T\) such that \(\alpha(t)\leq x(t)+l(t)-u(t)\leq ...
Venkat Anantharam, Takis Konstantopoulos
openaire   +2 more sources

A Completion for Partially Ordered Sets

Journal of the London Mathematical Society, 1969
A completion is obtained by imbedding any partially ordered set into its (completely distributive, complete) lattice of lower semi-ideals.
openaire   +2 more sources