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Fuss-Catalan Triangles (2310.07317v2)

Published 11 Oct 2023 in math.CO and math.GN

Abstract: For each $p>0$ we define by recurrence a triangle $Tp(n,k)$ whose rows sum to the Fuss-Catalan numbers $ \frac{1}{p n+1}\binom{pn+1}{n}$, generalizing the known Catalan triangle corresponding to the case $p=2$. (In fact, $Tp(n,k)$ has an explicit formula counting simple lattice paths). Moreover, for some small values of $p$, the signed sums turn out to be known sequences. \end{abstract}

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