منابع مشابه
Complexity of short generating functions
We give complexity analysis of the class of short generating functions (GF). Assuming #P 6⊆FP/poly, we show that this class is not closed under taking many intersections, unions or projections of GFs, in the sense that these operations can increase the bit length of coefficients of GFs by a super-polynomial factor. We also prove that truncated theta functions are hard in this class.
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Let a1, a2, . . . , an be distinct, positive integers with (a1, a2, . . . , an) = 1, and let k be an arbitrary field. Let H(a1, . . . , an; z) denote the Hilbert series of the graded algebra k[ta1 , ta2 , . . . , tan ]. We show that, when n = 3, this rational function has a simple expression in terms of a1, a2, a3; in particular, the numerator has at most six terms. By way of contrast, it is kn...
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ژورنال
عنوان ژورنال: Forum of Mathematics, Sigma
سال: 2018
ISSN: 2050-5094
DOI: 10.1017/fms.2017.29