A Pentagonal Number Sieve
A Pentagonal Number Sieve
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五边形数筛
DOI：
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发表时间：
1998
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通讯作者：
D. Zeilberger
中科院分区：
文献类型：
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作者：
S. Corteel;C. Savage;H. Wilf;D. Zeilberger
我们证明了一个一般的“五角筛”定理，其推论如下。首先，n的没有公共部分的划分对的数量是isp（n）2？p（n？1）2？p（n？2）2+p（n？5）2+p（n？（7）2？？第二，如果选择两个相同顶点数的未标记有根森林，那么它们没有共同树的概率是0.8705 .第三，当f，g是域GF（q）上两个同阶的一元多项式时，则f，g互素的概率为1？1/q。我们给出了明确的五角筛定理，推广早期的映射Bressoud和Zeilberger。
We prove a general “pentagonal sieve” theorem that has corollaries such as the following. First, the number of pairs of partitions of n that have no parts in common isp(n)2?p(n?1)2?p(n?2)2+p(n?5)2+p(n?7)2??.Second, if two unlabeled rooted forests of the same number of vertices are chosen i.u.a.r., then the probability that they have no common tree is .8705? . Third, iff,gare two monic polynomials of the same degree over the fieldGF(q), then the probability thatf,gare relatively prime is 1?1/q. We give explicit involutions for the pentagonal sieve theorem, generalizing earlier mappings found by Bressoud and Zeilberger.