Colorings with only rainbow arithmetic progressions

Autor:	János Pach, István Tomon
Rok vydání:	2020
Předmět:	BETA (programming language) Simple (abstract algebra) General Mathematics 010102 general mathematics Arithmetic progression Rainbow 010103 numerical & computational mathematics 0101 mathematics Arithmetic 01 natural sciences computer computer.programming_language Mathematics
Zdroj:	Acta Mathematica Hungarica. 161:507-515
ISSN:	1588-2632 0236-5294
DOI:	10.1007/s10474-020-01076-9
Popis:	If we want to color $$1,2,\ldots ,n$$ with the property that all 3-term arithmetic progressions are rainbow (that is, their elements receive 3 distinct colors), then, obviously, we need to use at least n/2 colors. Surprisingly, much fewer colors suffice if we are allowed to leave a negligible proportion of integers uncolored. Specifically, we prove that there exist $$\alpha ,\beta
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::626cdc682775613096d9c4d04ce4189d https://doi.org/10.1007/s10474-020-01076-9 Zobrazit plný text záznamu Plný text ve formátu PDF