论文标题
模块化大惊小怪的数字
Modular Fuss-Catalan numbers
论文作者
论文摘要
由Hein和Huang在2016年推出的模块化加泰罗尼亚数字$ c_ {k，n} $，计数$ x_0 * x_1 * x_1 * \ dots * x_n $，其中$ * $是二进制$ k $ - $ -SASCOCIATIVE操作，$ K $ $ K $是一个正整数。关联性的经典概念只是1个求解性，在这种情况下，$ c_ {1，n} = 1 $，唯一类的大小由加泰罗尼亚数字$ c_n $给出。在本文中，我们介绍了模块化的大惊小怪 - catalan编号$ c_ {k，n}^{m} $，该$ x_0 * x_1 * x_1 * \ dots * x_n $ whene $ * $是$ m $ $ k $ k $ - aSSociative for $ m \ geq geq 2 $。我们的主要结果是$ c_ {k，n}^{m} $的封闭公式和$ k $ - 求解的表征。
The modular Catalan numbers $C_{k,n}$, introduced by Hein and Huang in 2016 count equivalence classes of parenthesizations of $x_0 * x_1 * \dots *x_n$ where $*$ is a binary $k$-associative operation and $k$ is a positive integer. The classical notion of associativity is just 1-associativity, in which case $C_{1,n} = 1$ and the size of the unique class is given by the Catalan number $C_n$. In this paper we introduce modular Fuss-Catalan numbers $C_{k,n}^{m}$ which count equivalence classes of parenthesizations of $x_0 * x_1 * \dots *x_n$ where $*$ is an $m$-ary $k$-associative operation for $m \geq 2$. Our main results are a closed formula for $C_{k,n}^{m}$ and a characterisation of $k$-associativity.
