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- W2191115268 abstract "Given a coloring of Z + , we call a monochromatic set A = { a 1 < a 2 < ⋯ < a m } an m -set. The diameter of A is a m − a 1 . Given two m -sets A and B , we say that they are non-overlapping if max ( A ) < min ( B ) or max ( B ) < min ( A ) . The original study of non-overlapping m -sets, done by Bialostocki, Erdős, and Lefmann, concerned non-decreasing diameters. We investigate an “intermingling” of certain subset diameters of non-overlapping m -sets. In particular, we show that, for every integer m ≥ 2 , the minimum integer n ( m ) such that every 2-coloring of [ 1 , n ( m ) ] admits two m -sets { a 1 < a 2 < ⋯ < a m } and { b 1 < b 2 < ⋯ < b m } with a m < b 1 , such that b 1 − a 1 ≤ b 2 − a 2 ≤ ⋯ ≤ b m − a m is n ( m ) = 6 m − 5 . The r -coloring case is also investigated." @default.
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- W2191115268 date "2016-02-01" @default.
- W2191115268 modified "2023-10-14" @default.
- W2191115268 title "Intermingled ascending wave m-sets" @default.
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- W2191115268 doi "https://doi.org/10.1016/j.disc.2015.09.029" @default.
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