maths.free › Probability Theory › Applying Probability to Combinatorics › Small Ramsey Numbers
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.)
Ahora tú Ninguna calculadora resuelve este, pero las piezas son computables. Pruebe uno abajo, o escriba el suyo.
Una cuenta gratuita añade notas sobre cada lección, un registro de lo que has terminado, tus problemas resueltos en un lugar, y un tutor que puedes preguntar sobre esta página. Las matemáticas en sí están abiertas a todos, se han registrado o no.
Registrarse Inicio de sesiónSímbolos utilizados aquí
Toque cualquier símbolo para la definición completa, una imagen, y lo que cada letra en ella significa.
Preguntas que la gente hace
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.
Partes de esta página están adaptadas de Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). Condensados y re-explicados aquí; los errores son nuestros.
Más en Probability Theory
Sample spaces and the axiomsRandom variables and expectationThe common distributionsThe law of large numbers and the central limit theorem