A class of weighted Delannoy numbers
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913658534100992 |
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| author | Grau, J. M. Oller-Marcen, A. M Varona, J. L. |
| author_facet | Grau, J. M. Oller-Marcen, A. M Varona, J. L. |
| contents | The weighted Delannoy numbers are defined by the recurrence relation $f_{m,n}=αf_{m-1,n}+ βf_{m,n-1}+ γf_{m-1,n-1}$ if $m n>0 $, with $f_{m,n}=α^m β^n$ if $n m=0$. In this work, we study a generalization of these numbers considering the same recurrence relation but with $f_{m,n}=A^m B^n$ if $n m=0$. More particularly, we focus on the diagonal sequence $f_{n,n}$. With some ingenuity, we are able to make use of well-established methods by Pemantle and Wilson, and by Melczer in order to determine its asymptotic behavior in the case $A,B,α,β,γ\geq 0$. In addition, we also study its P-recursivity with the help of symbolic computation tools. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09726 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A class of weighted Delannoy numbers Grau, J. M. Oller-Marcen, A. M Varona, J. L. Combinatorics The weighted Delannoy numbers are defined by the recurrence relation $f_{m,n}=αf_{m-1,n}+ βf_{m,n-1}+ γf_{m-1,n-1}$ if $m n>0 $, with $f_{m,n}=α^m β^n$ if $n m=0$. In this work, we study a generalization of these numbers considering the same recurrence relation but with $f_{m,n}=A^m B^n$ if $n m=0$. More particularly, we focus on the diagonal sequence $f_{n,n}$. With some ingenuity, we are able to make use of well-established methods by Pemantle and Wilson, and by Melczer in order to determine its asymptotic behavior in the case $A,B,α,β,γ\geq 0$. In addition, we also study its P-recursivity with the help of symbolic computation tools. |
| title | A class of weighted Delannoy numbers |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2501.09726 |