Fuss-Catalan Triangles

2023/10/11 by Aicardi, Francesca
#05A10 #05A19 #57M50 #Combinatorics (math.CO) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2310.07317

Abstract

For each p>0 we define by recurrence a triangle T^p(n,k) whose rows sum to the Fuss-Catalan numbers (1)/(p n+1)\binompn+1n, generalizing the known Catalan triangle corresponding to the case p=2. (In fact, T^p(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. \endabstract

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