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Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical
THE MÖBIUS FUNCTION OF THE PERMUTATION PATTERN POSET
, 902
"... Abstract. A permutation τ contains another permutation σ as a pattern if τ has a subsequence whose elements are in the same order with respect to size as the elements in σ. This defines a partial order on the set of all permutations, and gives a graded poset P. We present some results on the Möbius ..."
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Cited by 13 (3 self)
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Abstract. A permutation τ contains another permutation σ as a pattern if τ has a subsequence whose elements are in the same order with respect to size as the elements in σ. This defines a partial order on the set of all permutations, and gives a graded poset P. We present some results on the Möbius
The topology of the permutation pattern poset
, 2014
"... The set of all permutations, ordered by pattern containment, forms a poset. This extended abstract presents the first explicit major results on the topology of intervals in this poset. We show that almost all (open) intervals in this poset have a disconnected subinterval and are thus not shellable ..."
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Cited by 2 (0 self)
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The set of all permutations, ordered by pattern containment, forms a poset. This extended abstract presents the first explicit major results on the topology of intervals in this poset. We show that almost all (open) intervals in this poset have a disconnected subinterval and are thus
Posets of Matrices and Permutations with Forbidden Subsequences
 ANNALS OF COMBINATORICS
, 2003
"... The enumeration of permutations with specific forbidden subsequences has applications in areas ranging from algebraic geometry to the study of sorting algorithms. We consider a ranked poset of permutation matrices whose global structure incorporates the solution to the equivalent problem of enumera ..."
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Cited by 4 (0 self)
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The enumeration of permutations with specific forbidden subsequences has applications in areas ranging from algebraic geometry to the study of sorting algorithms. We consider a ranked poset of permutation matrices whose global structure incorporates the solution to the equivalent problem
Permutation Statistics of Indexed and Poset Permutations
"... The definitions of descents and excedances in the elements of the symmetric group S d are generalized in two different directions. First, descents and excedances are defined for indexed permutations, i.e. the elements of the group S n d = Z n o S d , where o is wreath product with respect to the u ..."
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Cited by 11 (3 self)
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The definitions of descents and excedances in the elements of the symmetric group S d are generalized in two different directions. First, descents and excedances are defined for indexed permutations, i.e. the elements of the group S n d = Z n o S d , where o is wreath product with respect
THE STRUCTURE OF THE CONSECUTIVE PATTERN POSET
"... Abstract. The consecutive pattern poset is the infinite partially ordered set of all permutations where σ ≤ τ if τ has a subsequence of adjacent entries in the same relative order as the entries of σ. We study the structure of the intervals in this poset from topological, posettheoretic, and enumer ..."
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Abstract. The consecutive pattern poset is the infinite partially ordered set of all permutations where σ ≤ τ if τ has a subsequence of adjacent entries in the same relative order as the entries of σ. We study the structure of the intervals in this poset from topological, poset
Posets and permutations in the duplicationloss model: Minimal permutations with d descents
 CoRR
"... In this paper, we are interested in the combinatorial analysis of the whole genome duplication random loss model of genome rearrangement initiated in [8] and [7]. In this model, genomes composed of n genes are modelled by permutations of the set of integers [1..n], that can evolve through duplicati ..."
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Cited by 3 (2 self)
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duplicationloss steps. It was previously shown that the class of permutations obtained in this model after a given number p of steps is a class of patternavoiding permutations of finite basis. The excluded patterns were described as the minimal permutations with d = 2 p descents, minimal being intended
UNLABELED (2 + 2)FREE POSETS, ASCENT SEQUENCES AND PATTERN AVOIDING PERMUTATIONS
"... Abstract. We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2 + 2)free posets and a certain class of chord diagrams (or involutions), already appear in the literature. The third one is a class of permutations, defined in terms of a new type of ..."
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Cited by 67 (15 self)
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+ 2)free posets, chord diagrams and permutations. Our bijections preserve numerous statistics. We also determine the generating function of these classes of objects, thus recovering a series obtained by Zagier for chord diagrams. That this series also counts (2 + 2)free posets seems to be new
Results 1  10
of
2,890