Ramsey's theorem: Difference between revisions

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{{math|''R''(''r'', ''s'')}} with {{math|''r'', ''s'' ≤ 10}} are shown in the table below. Where the exact value is unknown, the table lists the best known bounds. {{math|''R''(''r'', ''s'')}} with {{math|''r'' < 3}} are given by {{math|1=''R''(1, ''s'') = 1}} and {{math|1=''R''(2, ''s'') = ''s''}} for all values of {{mvar|s}}.
 
The standard survey on the development of Ramsey number research is the ''Dynamic Survey 1'' of the ''[[Electronic Journal of Combinatorics]]'', by [[Stanisław Radziszowski]], which is periodically updated.<ref name="bananas">{{cite journal | url = http://www.combinatorics.org/ojs/index.php/eljc/article/view/DS1/pdf | title = Small Ramsey Numbers|doi=10.37236/21|doi-access=free|journal=Electronic Journal of Combinatorics|department=Dynamic Surveys|date=2011|last1=Radziszowski|first1=Stanisław| volume = 1000|author1-link=Stanisław Radziszowski}}</ref><ref name="sprSRS">{{cite web|url=https://www.cs.rit.edu/~spr/ElJC/eline.html|title=DS1|author=Stanisław Radziszowski|access-date=17 August 2023}}</ref> Where not cited otherwise, entries in the table below are taken from the January 2021 edition. (Note there is a trivial symmetry across the diagonal since {{math|1=''R''(''r'', ''s'') = ''R''(''s'', ''r'')}}.)
 
{| class="wikitable"