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تسجيل مستخدم جديدCounting number of factorizations of a natural number
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تأليف
Shamik Ghosh
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In this note we describe a new method of counting the number of unordered factorizations of a natural number by means of a generating function and a recurrence relation arising from it, which improves an earlier result in this direction.
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We show in this note that the average number of terms in the optimal double-base number system is in Omega(n / log n). The lower bound matches the upper bound shown earlier by Dimitrov, Imbert, and Mishra (Math. of Comp. 2008).
The Colour Refinement procedure and its generalisation to higher dimensions, the Weisfeiler-Leman algorithm, are central subroutines in approaches to the graph isomorphism problem. In an iterative fashion, Colour Refinement computes a colouring of th
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Let X be a projective curve over Q and t a non-constant Q-rational function on X of degree n>1. For every integer a pick a points P(a) on X such that t(P(a))=a. Dvornicich and Zannier (1994) proved that for large N the field Q(P(1), ..., P(N)) is of
degree at least exp(cN/log N) over Q, where c>0 depends only on X and t. In this note we extend this result, replacing Q by an arbitrary number field.
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