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- W4293703604 abstract "We investigate several functions related to the r-color off-diagonal van der Waerden numbers w(m1,…,mr), where w(m1,…,mr) is the minimal integer n such that every r-coloring of {1,2,…,n} admits an mi-term arithmetic progression with all terms of color i for some i∈{1,2,…,r}. We start by giving a new lower bound for these related numbers. Next, the exact values and bounds of numbers related to quasi-progressions and mixed quasi-progression-van der Waerden numbers are given. Then, inspired by the success of graph Gallai-Ramsey theory and rainbow arithmetic progressions, we introduce the concept of Gallai-van der Waerden numbers, and obtain some exact values and bounds for these numbers, some of which are derived by the probabilistic method and the Lovász Local Lemma." @default.
- W4293703604 created "2022-08-31" @default.
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- W4293703604 date "2023-01-01" @default.
- W4293703604 modified "2023-10-12" @default.
- W4293703604 title "Arithmetic progressions, quasi progressions, and Gallai-Ramsey colorings" @default.
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- W4293703604 doi "https://doi.org/10.1016/j.jcta.2022.105672" @default.
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