Shao, Zehui; Xu, Xiaodong On semi-progression van der Waerden numbers. (English) Zbl 1269.05111 Comput. Appl. Math. 32, No. 1, 19-25 (2013). Summary: In this note, a dynamic programming-like method is used to detect \(k\)-term semi-progression efficiently. By using this approach, we obtain some exact values and new lower bounds on semi-progression van der Waerden numbers. Cited in 1 Document MSC: 05D10 Ramsey theory 05D05 Extremal set theory 90C39 Dynamic programming 11B25 Arithmetic progressions Keywords:arithmetic progression; Szemerédi’s theorem; dynamic programming; semi-progression PDFBibTeX XMLCite \textit{Z. Shao} and \textit{X. Xu}, Comput. Appl. Math. 32, No. 1, 19--25 (2013; Zbl 1269.05111) Full Text: DOI References: [1] Graham RL, Rothschild BL, Spencer JH (1990) Ramsey Theory. Wiley, New York [2] Landman B, Robertson A (2004) Ramsey Theory on the Integers. American Mathematical Society, USA · Zbl 1035.05096 [3] Landman B (1998) Monochromatic sequences whose gaps belong to $$\(\backslash\){d,2d,\(\backslash\)cdots, md\(\backslash\)}$$ . Bull Aust Math Soc 58:93–101 · Zbl 0907.05054 · doi:10.1017/S0004972700032020 [4] Landman B, Robertson A, Culver C (2005) Some new exact van der Waerden numbers, Integers Electronic J Combinatorial Number Theory 5: #A10 · Zbl 1110.05097 [5] Shao Z, Deng F, Liang M, Xu X (2012) On sets without $$k$$ -term arithmetic progression. J Comput Sys Sci 78:610–618 · Zbl 1237.68262 · doi:10.1016/j.jcss.2011.09.003 [6] (2013) Van der Waerden numbers. http://www.st.ewi.tudelft.nl/sat/waerden.php · Zbl 1269.05111 [7] Kouril M, Paul JL (2008) The van der Waerden number W(2,6) is 1132. Exp Math 17(1):53–61 · Zbl 1151.05048 · doi:10.1080/10586458.2008.10129025 [8] Kouril M (2012) Computing the van der Waerden number W(3,4)=293, Integers Electronic J Combinatorial Number Theory 12: #A46. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.