منابع مشابه
Odd values of the partition function
Let p(n) denote the number of partitions of an integer n. Recently the author has shown that in any arithmetic progression r (mod t), there exist infinitely many N for which p(N) is even, and there are infinitely many M for which p(M) is odd, provided there is at least one such M. Here we construct finite sets of integers Mi for which p(Mi) is odd for an odd number of i. Whereas Euler’s recurre...
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Letp(n) be the number of partitions of an integern. Euler proved the following recurrence for p(n): p(n)= ∞ ∑ k=1 (−1)k+1 ( p ( n−ω(k))+p(n−ω(−k))), (∗) whereω(k)= (3k2+k)/2. In view of Euler’s result, one sees that it is fairly easy to compute p(n) very quickly. However, many questions remain open even regarding the parity of p(n). In this paper, we use various facts about elliptic curves and ...
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One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities (partition-function games). When externalities are present, not only can a player’s marginal contribution—a central notion to the Shapley value—be defined in a variety of ways, but it is also not obvious which axiomatization should be used. Consequently, a number of authors e...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00117-3