Results 111 to 120 of about 41,670 (161)

Partially Ordered Sets

2008
We introduce the notion of a partially ordered set (poset) we and define several types of special elements associated with partial orders.
Dan A. Simovici, Chabane Djeraba
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Partially Ordered Sets

1986
Partially ordered sets, or posets, appear in many branches of mathematics, but they are fundamental in combinatorics. For example, many of the important enumeration techniques (generating functions, inclusion-exclusion) have their theoretical foundation in some underlying poset.
Dennis Stanton, Dennis White
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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).
Duffus, Dwight, Łuczak, Tomasz, Rödl, Vojtěch, Ruciński, Andrzej   +3 more
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Partially ordered sets

2015
Apples and oranges. Sometimes things are incomparable. For breakfast, I like granola better than gruel. I like it even better when my granola has fresh fruit on top. I also like a nice omelette better than gruel. But on any given day I cannot say whether I would prefer granola (with or without fruit) or an omelette. I am only able to partially order my
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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 ...
Hanna, A. J., McMaster, T. B. M.
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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-
Billera, Louis J., Hetyei, Gábor
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Partially Ordered Sets

1988
The present chapter gives some mathematical theory of partially ordered sets. Referring to the appendix on terminology, we recall that a partially ordered set is a pair (X, ≺) where ≺ is an irreflexive and transitive relation on X. We shall not immediately give the interpretation of the elements of X.
Eike Best, César C. Fernández
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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.
Banaschewski, Bernhard, Nelson, Evelyn
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Homomorphism-Homogeneous Partially Ordered Sets

Order, 2007
A homomorphism between posets \((A,\leq)\) and \((B,\leq)\) is a map preserving the ordering \(\leq\). A poset \(P\) is called homomorphism-homogeneous if every homomorphism \(A\to B\) of sub-posets \(A,B\subset P\) can be extended to a homomorphism \(P\to P\).
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P-Faithful Partially Ordered Sets

Ukrainian Mathematical Journal, 2002
Summary: We prove a theorem that describes \(P\)-faithful partially ordered sets.
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