一种求Ramsey数的命题演算法

A Propositional Calculus Method to Find Ramsey Numbers

关键词:  Ramsey数  命题演算  三角矩阵

Key words:  Ramsey number  prepositional calculus  triangle matrix

摘要:

首先在矩阵中用谓词描述"含K_n"和"含K_m",然后通过命题演算法逐行求出不含K_n也不含K_m的矩阵(a_ij)_j=i+1,…,l^{i=1,2,…,l-1}.若对于l ≤ r-1有这样的矩阵,而对于l=r却没有,则r为Ramsey数.

Abstract:

The "include K_n and K_m" in a matrix are firstly described by predicate. Then the matrix (a_ij)_{j=i+ 1,…,l}^{i=1,2,…,l-1} that include neither K_n,nor K_m,is found by a prepositional calculus in row by row. If there are the matrixes for l ≤ r-1,but there is no the matrix for l=r,then r is Ramsey number.