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Good sequences of integers

โœ Scribed by David Carlson


Publisher
Elsevier Science
Year
1975
Tongue
English
Weight
518 KB
Volume
7
Category
Article
ISSN
0022-314X

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## Combinatorialists are interested in sequences of integers which count things. We often find that the same sequence counts two families of things with no obvious connection, or that a simple translation connects the answers to two counting problems. In this way, unexpected connections have come

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For k>2 and r 2, let G(k, r) denote the smallest positive integer g such that every increasing sequence of g integers [a 1 , a 2 , ..., a g ] with gaps a j+1 &a j # [1, ..., r], 1 j g&1 contains a k-term arithmetic progression. Brown and Hare proved that G(k, 2)>-(k&1)ร‚2 ( 43 ) (k&1)ร‚2 and that G(k,