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general.hpp File Reference

General plans regarding Ramsey theory (in computer algebra) More...

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## Detailed Description

General plans regarding Ramsey theory (in computer algebra)

Todo:
Systematic notations for the numbers in Ramsey theory : DONE
• DONE Currently we have Ramsey, van-der-Waerden and Green-Tao numbers.
• DONE Those numbers appear in plans, (soon) as functions (computing them), and in Latex-documents.
• DONE (we follow these conventions) For the plans-file (and other ascii-code) I propose ramsey_s^r(...), vanderwaerden_m(...) and greentao_m(...), following the usage of the latter two functions as it is already established:
1. s resp. m is the number of "colours" (or parts)
2. "..." is either one number in case of diagonal problems, or a list of s resp. m numbers.
3. r is the hyperedge-length.
• DONE Maxima functions:
1. DONE For the Maxima function I propose ramsey([r,[...]]), vanderwaerden([...]) and greentao([...]), while in case of diagonal problems we use vanderwaerdend(m,k) resp. greentaod(m,k) resp. ramseyd(s,r,k) is used.
2. DONE (no redundancy) Shall we keep the s resp. m? It is redundant except of the diagonal cases.
3. DONE (no, but special functions for the diagonal cases) We could always write out the diagonal cases? Perhaps this is best.
4. DONE If only bounds are known, then the return value is a pair consisting of lower and upper bound.
• DONE The various generators for hypergraphs and clause-sets should be adapted to these new notions:
1. The order of parameters should be as above.
2. Keeping, as we have it now, a "2" in the name for the case of k=2 (where then this parameter is no longer used).
3. n is always appended to the end of the parameter list.
• DONE For Latex we introduce macros {s}{r}{...}, {m}{...} and {m}{...}, where for the output "ram_k^r", "vdw_k" and "grt_k" is used.
• See the plans on the machinery for providing Ramsey-numbers in ComputerAlgebra/RamseyTheory/Lisp/Ramsey/plans/Numbers.hpp.

Definition in file general.hpp.