A Fast Algorithm for Denumerants with Three Variables
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910117548523520 |
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| author | Liu, Feihu Xin, Guoce |
| author_facet | Liu, Feihu Xin, Guoce |
| contents | Let $a,b,c$ be distinct positive integers such that $a<b<c$ and $\gcd(a,b,c)=1$. For any non-negative integer $n$, the denumerant function $d(n;a,b,c)$ denotes the number of solutions of the equation $ax_1+bx_2+cx_3=n$ in non-negative integers $x_1,x_2,x_3$. We present an algorithm that computes $d(n;a,b,c)$ with a time complexity of $O(\log b)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18955 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Fast Algorithm for Denumerants with Three Variables Liu, Feihu Xin, Guoce Combinatorics Number Theory Let $a,b,c$ be distinct positive integers such that $a<b<c$ and $\gcd(a,b,c)=1$. For any non-negative integer $n$, the denumerant function $d(n;a,b,c)$ denotes the number of solutions of the equation $ax_1+bx_2+cx_3=n$ in non-negative integers $x_1,x_2,x_3$. We present an algorithm that computes $d(n;a,b,c)$ with a time complexity of $O(\log b)$. |
| title | A Fast Algorithm for Denumerants with Three Variables |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2406.18955 |