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- W1574979076 abstract "In this paper, we are concerned with calculating $r(k, n)$, the length of the longest $k$-AP free subsequences in $1, 2, ldots , n$. We prove the basic inequality $r(k, n) le n − lfloor m/2rfloor$, where $n = m(k − 1) + r$ and $r < k − 1$. We also discuss a generalization of a famous conjecture of Szekeres (as appears in Erdős and Turán) and describe a simple greedy algorithm that appears to give an optimal $k$-AP free sequence infinitely often. We provide many exact values of $r(k, n)$ in the Appendix." @default.
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- W1574979076 date "2013-12-17" @default.
- W1574979076 modified "2023-09-30" @default.
- W1574979076 title "Unique Sequences Containing No $k$-Term Arithmetic Progressions" @default.
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- W1574979076 doi "https://doi.org/10.37236/3007" @default.
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