一句话：用基于多重集的无元素方法重构 Ewens 分布理论，提出划分多项式定理与无元素多项分布。
本文重新发展与深化了 1970 年代群体生物学中 Ewens 等人的概率论，其核心是描述生物突变的 Ewens 分布。原始工作以自然数上的特殊多重集——划分——来表述；本文则从任意集合上的多重集出发，把划分视为只刻画「重数的重数」而不指名元素本身的一种特殊形式，并让这套「无元素」进路与通常的基于元素的理论并行展开。Ewens 著名的抽样公式刻画了划分上一个（带参数的）分布锥；本文用新的无元素多项分布给出该链的另一个锥。这些分布之所以良定义，依赖于一个新颖的「划分多项式定理」，它推广了熟悉的多项式定理，其基础是作为无元素分布的「除法」新概念，即由和为 1 的概率所构成的多重集。
This article redevelops and deepens the probability theory of Ewens and others from the 1970s in population biology. At the heart of this theory are the so-called Ewens distributions describing biolological mutations. These distributions have a particularly rich (and beautiful) mathematical structure. The original work is formulated in terms of partitions, which are special multisets on natural numbers. The current redevelopment starts from multisets on arbitrary sets, with partitions as a special form that captures only the multiplicities of multiplicities, without naming the elements themselves. This ‘element-free’ approach will be developed in parallel to the usual element-based theory. Ewens’ famous sampling formula describes a cone of (parametrised) distributions on partitions. Another cone for this chain is described in terms of new (element-free) multinomials. They are well-defined because of a novel ‘partitions multinomial theorem’ that extends the familiar multinomial theorem. This is based on a new concept of ‘division’, as element-free distribution, in terms of multisets of probabilities that add up to one.