Displaying similar documents to “A Pfaffian-Hafnian analogue of Borchardt's identity.”

Determinants of matrices associated with incidence functions on posets

Shaofang Hong, Qi Sun (2004)

Czechoslovak Mathematical Journal

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Let S = { x 1 , , x n } be a finite subset of a partially ordered set P . Let f be an incidence function of P . Let [ f ( x i x j ) ] denote the n × n matrix having f evaluated at the meet x i x j of x i and x j as its i , j -entry and [ f ( x i x j ) ] denote the n × n matrix having f evaluated at the join x i x j of x i and x j as its i , j -entry. The set S is said to be meet-closed if x i x j S for all 1 i , j n . In this paper we get explicit combinatorial formulas for the determinants of matrices [ f ( x i x j ) ] and [ f ( x i x j ) ] on any meet-closed set S . We also obtain necessary and sufficient conditions for...

Inequality-sum : a global constraint capturing the objective function

Jean-Charles Régin, Michel Rueher (2005)

RAIRO - Operations Research - Recherche Opérationnelle

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This paper introduces a new method to prune the domains of the variables in constrained optimization problems where the objective function is defined by a sum y = Σ x i , and where the integer variables x i are subject to difference constraints of the form x j - x i c . An important application area where such problems occur is deterministic scheduling with the mean flow time as optimality criteria. This new constraint is also more general than a sum constraint defined on a set of ordered variables. Classical...