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Splittability for Partially Ordered Sets
Order, 2000This 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 ...
A. J. Hanna, T. B. M. McMaster
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Decompositions of Partially Ordered Sets
Order, 2000In 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-
Gábor Hetyei, Louis J. Billera
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, 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.
César Fernández, Eike Best
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Component partially ordered sets [PDF]
Mathematical Notes of the Academy of Sciences of the USSR, 1971 Properties of component partially ordered sets (i.e., dense subsets of Boolean algebras) are used to construct mappings of Boolean algebras generalizing the idea of homomorphisms; the properties of a minimal Boolean algebra generated by a given component partially ordered set are investigated.
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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 E. White
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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 E. White
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Endomorphisms of Partially Ordered Sets
Combinatorics, Probability and Computing, 1998It 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).
Vojtěch Rödl +3 more
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Molecules of a partially ordered set
Algebra Universalis, 1981It is shown that in a general partially ordered set (P, ≤) the notion of a molecule (i.e., a nonzero elementm ofP such that any two nonzero elements ofP which are ≤m have a nonzero lower bound) is in close analogy to the notion of an atom in a Boolean ring.
Alexander Abian, Alexander Abian
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Completions of Partially Ordered Sets
SIAM Journal on Computing, 1982We 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.
Evelyn Nelson, Bernhard Banaschewski
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Partial orderings for sets of multisets
Algebra Universalis, 1985It is shown that if \((S,
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