Geodesic
A Construction for Partitions Which Avoid Long Arithmetic Progressions
Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 409-414

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For k ≥2, t ≥2, let W(k, t) denote the least integer m such that in every partition of m consecutive integers into k sets, atleast one set contains an arithmetic progression of t+1 terms. This paper presents a construction which improves the best previously known lower bounds on W(k, t) for small k and large t. 
Berlekamp, E.R. A Construction for Partitions Which Avoid Long Arithmetic Progressions. Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 409-414. doi: 10.4153/CMB-1968-047-7
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     title = {A {Construction} for {Partitions} {Which} {Avoid} {Long} {Arithmetic} {Progressions}},
     journal = {Canadian mathematical bulletin},
     pages = {409--414},
     year = {1968},
     volume = {11},
     number = {3},
     doi = {10.4153/CMB-1968-047-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-047-7/}
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