Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2604.02115 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
Tabla de Contenidos:
- A constellation pattern is a finite increasing rational sequence \(Q=[0=q_0<q_1<\cdots<q_k=1]\), and a \(Q\)-constellation in \([n]\) is obtained by scaling and translating a rational pattern $Q$, with key examples including arithmetic progressions. In 2010, Butler, Costello, and Graham proposed a conjecture, that is, for any constellation pattern $Q$ there is a coloring pattern of $[n]$ that has $γn^2+o\left(n^2\right)$ monochromatic constellations, where $γ$ is smaller than the coefficient for a random coloring. In this paper, we confirm this conjecture. As applications of this conjecture, we obtain interval-uncommon translation-invariant linear systems associated with rational constellations and a ground-state bound for deterministic arithmetic hypergraph spin systems.