Computing Parametric Rational Generating Functions with a Primal Barvinok Algorithm
نویسندگان
چکیده
منابع مشابه
Computing Parametric Rational Generating Functions with a Primal Barvinok Algorithm
Computations with Barvinok’s short rational generating functions are traditionally being performed in the dual space, to avoid the combinatorial complexity of inclusion–exclusion formulas for the intersecting proper faces of cones. We prove that, on the level of indicator functions of polyhedra, there is no need for using inclusion–exclusion formulas to account for boundary effects: All linear ...
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We examine two different ways of encoding a counting function, as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input variables of the (quasi-polynomial) function are fixed, there is a polynomial time algorithm which converts between the two representations. Examples of such countin...
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In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. H. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables.The present article, starting from the ...
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Many of the positive results in this paper are derived from results from the literature on rational generating functions and in particular from the method of Barvinok and Woods [2]. Generating functions have been applied in an analogous fashion in a variety of other contexts, including social choice theory [7], discrete optimization [6], combinatorics [4], and compiler optimization [8]. We here...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2008
ISSN: 1077-8926
DOI: 10.37236/740