Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.07317 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911782462816256 |
|---|---|
| author | Aicardi, Francesca |
| author_facet | Aicardi, Francesca |
| contents | For each $p>0$ we define by recurrence a triangle $T^p(n,k)$ 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, $T^p(n,k)$ has an explicit formula counting simple lattice paths). Moreover, for some small values of $p$, the signed sums turn out to be known sequences. \end{abstract} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07317 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fuss-Catalan Triangles Aicardi, Francesca Combinatorics General Topology 05A10, 05A19, 57M50 For each $p>0$ we define by recurrence a triangle $T^p(n,k)$ 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, $T^p(n,k)$ has an explicit formula counting simple lattice paths). Moreover, for some small values of $p$, the signed sums turn out to be known sequences. \end{abstract} |
| title | Fuss-Catalan Triangles |
| topic | Combinatorics General Topology 05A10, 05A19, 57M50 |
| url | https://arxiv.org/abs/2310.07317 |