A BUDGET OF RHYME SCHEME COUNTS 1
A BUDGET OF RHYME SCHEME COUNTS 1
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RHYME 计划的预算至关重要 1
DOI：
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发表时间：
1979
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影响因子：
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通讯作者：
J. Riordan
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文献类型：
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作者：
J. Riordan
押韵方案，也许是背景和钟声数字背后最古老的组合设置，通过这种列举预算从目前的忽视中拯救了出来。N节诗节的押韵方案是一个(数字)序列(r1，r2，…，Rn)，其中Rj可以是1、2、…中的任何一个，Dj-1+1，其中Dj表示R1、…，Rj，n=3的押韵模式为：111,112,121,122,123。当然，n节的方案总数是Bell数Bn。它们有一个集合划分的平凡映射，但在序列研究中常见的一些枚举在被重新表述为集合划分时是奇怪的(甚至是愚蠢的)。所显示的预算(决不是穷尽的)是因为它对贝尔和斯特林数字的研究感兴趣。一个令人惊讶的是精致的贝尔多变量多项式的出现。
Rhyme schemes, perhaps the oldest combinatorial setting behind the Setting and Bell numbers, are rescued from current neglect by this budget of enumerations. A rhyme scheme for a stanza of n verses is a (number) sequence (r1, r2, …, rn) in which rj may be any of 1, 2, …, dj‐1+ 1, with dj the number of distinct numbers among r1, …, rj, the rhyme schemes for n= 3 are: 111, 112, 121, 122, 123. The total number of schemes for n verses is of course the Bell number Bn. They have a trivial mapping of set‐partitions but some enumerations familiar in the study of sequences are odd (even idiotic) when rephrased as set‐partitions. The budget displayed (by no means exhaustive) is selected for its interest in the study of Bell and Stirling numbers. One surprise is the appearance of refined Bell multivariable polynomials.