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Small Ramsey Numbers
Actually determining the Ramsey numbersR(m,n)Ramsey number R(m,n) referenced in seems to be a notoriously difficult problem, and only a handful of these values are known precisely.
Small Ramsey Numbers
Actually determining the Ramsey numbers\(R(m,n)\)Ramsey number \(R(m,n)\) referenced in seems to be a notoriously difficult problem, and only a handful of these values are known precisely. In particular, \(R(3,3)=6\) and \(R(4,4)=18\), while \(43\le R(5,5)\le 49\). The distinguished Hungarian mathematician Paul Erdős said on many occasions that it might be possible to determine \(R(5,5)\) exactly, if all the world's mathematical talent were to be focused on the problem. But he also said that finding the exact value of \(R(6,6)\) might be beyond our collective abilities.
In the following table, we provide information about the Ramsey numbers \(R(m,n)\) when \(m\) and \(n\) are at least \(3\) and at most \(9\). When a cell contains a single number, that is the precise answer. When there are two numbers, they represent lower and upper bounds.
For additional (or more current) data, see Dynamic Survey #DS1: Small Ramsey Numbers by Stanisław Radziszowski in the Electronic Journal of Combinatorics. ( was last updated using the 12 January 2014 version of that article.)
Ҳоло шумо Ҳеҷ ҳисобкунак инро ҳал намекунад, лекин қисмҳои он ҳисобшавандаанд. Яке аз инҳоро дар поён санҷед ё худи худро ворид кунед.
Дар ҳисоби ройгон ба ҳар як дарс қайдҳо илова карда мешаванд, қайди он, ки шумо чӣ кор кардаед, масъалаҳои ҳалшуда дар як ҷо ва муаллиме, ки шумо метавонед дар бораи ин саҳифа пурсед. Математика барои ҳама кушода аст, хоҳ ворид шуда бошад ё на.
Бақайдгирӣ Ворид шуданСимволы, используемые здесь
Барои муайянкунии пурраи маъно, тасвир ва маънои ҳар як ҳарф дар он, ба ҳар як аломат пахш кунед.
Саволҳои маъмул
What is the difference between probability and statistics?
Probability goes from a known model to what the data should look like; statistics goes from data back to the model. Probability theory is the deductive half.
What does the law of large numbers promise?
That the average of many independent samples converges to the expected value. It says nothing about any single trial.
Қисми ин саҳифа аз Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). Дар ин ҷо барои мо чизе нест, ки мо ба он бирасем.
& Иловаи забон Probability Theory
Sample spaces and the axiomsRandom variables and expectationThe common distributionsThe law of large numbers and the central limit theorem