奥卡姆剃刀的组合数学

摘要：

奥卡姆剃刀告诉我们要选择最简单的模型来符合我们的观察。为了在数学上理解他的过程，我们在函数偏序集的上下文中解释它。我们的方法导致了一些不寻常的新的组合问题，有限集之间的功能。同样的想法也被用来定义一个行为良好、显然未知的群体等级的类似物。我们还构造了一个与每个群相关联的无穷序列，称为其融合序列。这个序列中的首项由群的秩决定，我们提供了后续项的例子，这些例子表明这些数字与群的结构之间存在微妙的关系。

英文摘要：

Occam's Razor tells us to pick the simplest model that fits our observations. In order to make sense of his process mathematically, we interpret it in the context of posets of functions. Our approach leads to some unusual new combinatorial problems concerning functions between finite sets. The same ideas are used to define a nicely behaved and apparently unknown analogue of the rank of a group. We also make a construction that associates with each group an infinite sequence of numbers called its fusion sequence. The first term in this sequence is determined by the rank of the group and we provide examples of subsequent terms that suggest a subtle relationship between these numbers and the structure of the group.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。