On Monochromatic Solutions of Linear Equations Using At Least Three Colors
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916810999201792 |
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| author | Wijaya, Laurence P. |
| author_facet | Wijaya, Laurence P. |
| contents | We study the number of monochromatic solution to linear equation in $\{1,\dots,n\}$ when we color the set by at least three colors. We consider the $r$-commonness for $r\geq 3$ of linear equation with odd number of terms, and we also prove that any $2$-uncommon equation is $r$-uncommon for any $r\geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Monochromatic Solutions of Linear Equations Using At Least Three Colors Wijaya, Laurence P. Combinatorics Number Theory 05D10, 05E16, 11B75 We study the number of monochromatic solution to linear equation in $\{1,\dots,n\}$ when we color the set by at least three colors. We consider the $r$-commonness for $r\geq 3$ of linear equation with odd number of terms, and we also prove that any $2$-uncommon equation is $r$-uncommon for any $r\geq 3$. |
| title | On Monochromatic Solutions of Linear Equations Using At Least Three Colors |
| topic | Combinatorics Number Theory 05D10, 05E16, 11B75 |
| url | https://arxiv.org/abs/2501.17136 |