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Sorting and Selection in Posets
, 2007
"... Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant in applications related to rankings in sports, college admi ..."
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Cited by 13 (0 self)
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Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant in applications related to rankings in sports, college
Tchebyshev posets
 Discrete Comput. Geom
"... Dedicated to Louis Billera on his sixtieth birthday We construct for each n an Eulerian partially ordered set Tn of rank n + 1 whose ceindex provides a noncommutative generalization of the nth Tchebyshev polynomial. We show that the order complex of each Tn is shellable, � homeomorphic to a spher ..."
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sphere, and that its face numbers minimize the expression max x≤1 � �n j=0 (fj−1/fn−1) · 2−j · (x − 1) j � among the fvectors of all (n − 1)dimensional simplicial complexes. The duals of the posets constructed have a recursive structure similar to face lattices of simplices or cubes, offering
Covering Linear Orders with Posets
"... Much research has been done on the combinatorial problem of generating the linear extensions of a given poset. This paper focuses on the reverse of that problem, where the input is a set of linear orders, and the goal is to construct a poset or set of posets that generates the input. Such a problem ..."
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Much research has been done on the combinatorial problem of generating the linear extensions of a given poset. This paper focuses on the reverse of that problem, where the input is a set of linear orders, and the goal is to construct a poset or set of posets that generates the input. Such a problem
The regular algebra of a poset
 Trans. Amer. Math. Soc
"... Abstract. Let K be a fixed field. We attach to each finite poset P a von Neumann regular Kalgebra QK(P) in a functorial way. We show that the monoid of isomorphism classes of finitely generated projective QK(P)modules is the abelian monoid generated by P with the only relations given by p = p + q ..."
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Cited by 6 (4 self)
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Abstract. Let K be a fixed field. We attach to each finite poset P a von Neumann regular Kalgebra QK(P) in a functorial way. We show that the monoid of isomorphism classes of finitely generated projective QK(P)modules is the abelian monoid generated by P with the only relations given by p = p + q
An AntiRamsey Theorem on Posets
"... It is known that if P and Q are posets and is lexicographic product, then (in the Erd}osRado partition notation), PQ ! (P; Q). ..."
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It is known that if P and Q are posets and is lexicographic product, then (in the Erd}osRado partition notation), PQ ! (P; Q).
The Poset of Hypergraph Quasirandomness
, 2012
"... Chung and Graham began the systematic study of hypergraph quasirandom properties soon after the foundational results of Thomason and ChungGrahamWilson on quasirandom graphs. One feature that became apparent in the early work on hypergraph quasirandomness is that properties that are equivalent for ..."
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Cited by 4 (2 self)
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the relationship between these quasirandom properties. We completely determine the poset of implications between essentially all hypergraph quasirandom properties that have been studied in the literature. This answers a recent question of Chung, and in some sense completes the project begun by Chung and Graham
The Dyck pattern poset
, 2014
"... We introduce the notion of pattern in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the patterncontainment relation defines a poset structure on the set of all Dyck paths, which we call the Dyck pattern poset. Given a Dyc ..."
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Cited by 2 (0 self)
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We introduce the notion of pattern in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the patterncontainment relation defines a poset structure on the set of all Dyck paths, which we call the Dyck pattern poset. Given a
On Entropy and Extensions of Posets
, 2011
"... A vast body of literature in combinatorics and computer science aims at understanding the structural properties of a poset P implied by placing certain marginal constraints on the uniform distribution over linear extensions of P. These questions are typically concerned with whether or not P must be ..."
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A vast body of literature in combinatorics and computer science aims at understanding the structural properties of a poset P implied by placing certain marginal constraints on the uniform distribution over linear extensions of P. These questions are typically concerned with whether or not P must
Geometric Applications of Posets
, 1998
"... We show the power of posets in computational geometry by solving several problems posed on a set S of n points in the plane: (1) find the n \Gamma k \Gamma 1 rectilinear farthest neighbors (or, equivalently, k nearest neighbors) to every point of S (extendable to higher dimensions), (2) enumerate th ..."
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We show the power of posets in computational geometry by solving several problems posed on a set S of n points in the plane: (1) find the n \Gamma k \Gamma 1 rectilinear farthest neighbors (or, equivalently, k nearest neighbors) to every point of S (extendable to higher dimensions), (2) enumerate
Results 1  10
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2,177