English

An equation for the general Ramsey number R(p1,p2,...pt;r)

Combinatorics 2011-08-09 v2 Logic

Abstract

The Ramsey number R(P1,P2,...,Pt;r)R(P_1,P_2,...,P_t;r) is a valve value such that as long as the cardinality nn of the nn-set Vn=1,...,nV_n={1,...,n} is no less than RR,however all the (nr)\binom{n}{r} rr-subsets of VnV_n are distributed into tt boxes, VnV_n will always have a property WW expressed as eq.(1).Thus, by calculating the number of ways of distribution of rr-subsets that makes WW true,one can get an equation for R(P1,P2,...,Pt;r)R(P_1,P_2,...,P_t;r).The evaluation of the general term in this eq. and the counting of the frequencies of occurrence of the various values the general term takes can be reduced to the problem of elementary counting.

Keywords

Cite

@article{arxiv.1009.1207,
  title  = {An equation for the general Ramsey number R(p1,p2,...pt;r)},
  author = {Kunjun Song},
  journal= {arXiv preprint arXiv:1009.1207},
  year   = {2011}
}

Comments

Version 2 with one crucial error corrected