局部受限组合物IV。几乎自由的大零件和无间隙
Locally Restricted Compositions IV. Nearly Free Large Parts and Gap-Freeness
摘要：
我们定义了局部限制合成的渐近自由的概念，这大致意味着大的部分通常可以被任何更大的部分取代。两个著名的例子是Carlitz和交替合成。我们表明，大部分具有渐近几何分布。这将导致渐近独立的泊松变量的数量的各种大的部分。在此基础上，我们得到的渐近公式是间隙自由的概率和期望值的最大部分，不同部分的数量和部分的多重数k，所有精确到o（1）。
英文摘要：
We define the notion of asymptotically free for locally restricted compositions, which means roughly that large parts can often be replaced by any larger parts. Two well-known examples are Carlitz and alternating compositions. We show that large parts have asymptotically geometric distributions. This leads to asymptotically independent Poisson variables for numbers of various large parts. Based on this we obtain asymptotic formulas for the probability of being gap free and for the expected values of the largest part, number of distinct parts and number of parts of multiplicity k, all accurate to o(1).
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