Integrals, partitions, and cellular automata
نویسندگان
چکیده
منابع مشابه
Integrals, Partitions, and Cellular Automata
We prove that ∫ 1 0 − log f(x) x dx = π 3ab where f(x) is the decreasing function that satisfies fa − f b = xa − xb, for 0 < a < b. When a is an integer and b = a + 1 we deduce several combinatorial results. These include an asymptotic formula for the number of integer partitions not having a consecutive parts, and a formula for the metastability thresholds of a class of threshold growth cellul...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2003
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-03-03417-2