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- W3039593090 abstract "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." @default.
- W3039593090 created "2020-07-10" @default.
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- W3039593090 date "2020-07-01" @default.
- W3039593090 modified "2023-09-27" @default.
- W3039593090 title "Modular Fuss-Catalan numbers." @default.
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