A method for proving polynomial enumeration formulas
نویسندگان
چکیده
منابع مشابه
A method for proving polynomial enumeration formulas
We present an elementary method for proving enumeration formulas which are polynomials in certain parameters if others are fixed and factorize into distinct linear factors over Z. Roughly speaking the idea is to prove such formulas by “explaining” their zeros using an appropriate combinatorial extension of the objects under consideration to negative integer parameters. We apply this method to p...
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The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic exists, but a proof in that system may include infinitely many formulas. In this note we describe a relationship between the validity of infinitary formulas in ...
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Counting the number of elements in finite sets Si (where i typically ranges over some index set I such as the non–negative integers or a cartesian product of the non–negative integers) is surely one of the oldest and most fundamental problems in mathematics. It is in the nature of the subject that only a few enumeration problems have a compact solution in terms of a simple explicit formula in i...
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Let f(x1, . . . , xk) be a polynomial over a field K. This paper considers such questions as the enumeration of the number of nonzero coefficients of f or of the number of coefficients equal to α ∈ K∗. For instance, if K = Fq then a matrix formula is obtained for the number of coefficients of fn that are equal to α ∈ Fq , as a function of n. Many additional results are obtained related to such ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2005
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2004.11.007