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On the Asymptotic Minimum Number of Monochromatic 3-Term Arithmetic Progressions by Pablo A. Parrilo; Aaron Robertson; Dan Saracino is a Mathematics article available to read on EtoBox.

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Let V (n) be the minimum number of monochromatic 3-term arithmetic progressions in any 2-coloring of {1, 2, . . . , n}. We show that 1675 32 768 As a consequence, we find that V (n) is strictly greater than the corresponding number for Schur triples (which is 1 22 n 2 (1 + o(1))). Additionally, we disprove the conjecture that V (n) = 1 16 n 2 (1 + o(1)) as well as a more general conjecture.

Who reads On the Asymptotic Minimum Number of Monochromatic 3-Term Arithmetic Progressions?

Author

Pablo A. Parrilo; Aaron Robertson; Dan Saracino

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0097-3165)

Published

2008

Language

EN

Field

Mathematics (Physical Sciences)