PICK'S FORMULA AND GENERALIZED EHRHART QUASI-POLYNOMIALS
نویسندگان
چکیده
منابع مشابه
Generalized Ehrhart Polynomials
Let P be a polytope with rational vertices. A classical theorem of Ehrhart states that the number of lattice points in the dilations P (n) = nP is a quasi-polynomial in n. We generalize this theorem by allowing the vertices of P (n) to be arbitrary rational functions in n. In this case we prove that the number of lattice points in P (n) is a quasi-polynomial for n sufficiently large. Our work w...
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To count the number of chemical compositions of a particular mass, we consider an alphabet A with a mass function which assigns a mass to each letter in A. We then compute the mass of a word (an ordered sequence of letters) by adding the masses of the constituent letters. Our main interest is to count the number of words that have a particular mass, where we ignore the order of the letters with...
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Numerous problems in program analysis, can be reduced to finding bounds on the number of integer points in a convex set, or the solution of a more general polyhedral counting problem. For a large class of applications the solution of such a counting problem can be expressed as a piecewise Ehrhart quasi-polynomial in the parameters. This work presentsmethods to find bounds on quasi-polynomials o...
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A quasi-polynomial is a function defined of the form q(k) = c d (k) k d + c d−1 (k) k d−1 + · · · + c0(k), where c0, c1,. .. , c d are periodic functions in k ∈ Z. Prominent examples of quasi-polynomials appear in Ehrhart's theory as integer-point counting functions for rational polytopes, and McMullen gives upper bounds for the periods of the cj (k) for Ehrhart quasi-polynomials. For generic p...
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A quasi-polynomial is a function defined of the form q(k) = cd(k) k d + cd−1(k) k d−1 + · · · + c0(k), where c0, c1, . . . , cd are periodic functions in k ∈ Z. Prominent examples of quasipolynomials appear in Ehrhart’s theory as integer-point counting functions for rational polytopes, and McMullen gives upper bounds for the periods of the cj(k) for Ehrhart quasi-polynomials. For generic polyto...
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ژورنال
عنوان ژورنال: Journal of the Indonesian Mathematical Society
سال: 2015
ISSN: 2460-0245,2086-8952
DOI: 10.22342/jims.21.2.192.71-75