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Abstract
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For
, a sequence
is called a
-diffsequence
if
for all
. Given a positive
integer
, we
say that
is
-accessible if
every
-coloring
of
admits arbitrarily long monochromatic
-diffsequences. If
every
-coloring
of
admits arbitrarily long monochromatic
arithmetic progressions
, ,
, with
, we say
that
is
-large. We prove
some new results on accessibility. We also define a property that is stronger than accessibility but
weaker than largeness, and study the connections among these various properties. The paper also
includes bounds, as well as tables of exact values, for the associated Ramsey functions for some
specific choices of .
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Keywords
van der Waerden, diffsequence, Ramsey theory
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Mathematical Subject Classification
Primary: 05D10, 11B25
Secondary: 11B39
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Milestones
Received: 21 January 2023
Accepted: 11 June 2023
Published: 23 September 2023
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© 2023 MSP (Mathematical Sciences
Publishers). |
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