Plans for Maximagenerators related to Hindman problems (and generalisations)
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Detailed Description
Plans for Maximagenerators related to Hindman problems (and generalisations)
 Todo:
 Improve generator names

The current names are rather unsystematic.

Also the notion of "degeneration" needs to be replaced by "injective" (appropriately).

DONE hindman2_nbfcsud(r,n) is for hindmani_r(2).

This function should be called hindmani_a1k2_nbfcsud(r,n).

DONE hindman2d_nbfcsud(r,n) is for hindman_r(2).

This function should be called hindman_a1k2_nbfcsud(r,n).

Shouldn't we have these functions just for general a? Then called hindman_k2_nbfcsud(a,r,n) and hindmani_k2_nbfcsud(a,r,n).

And likely we should just have hindman_nbfcsud(a,r,k,n) and hindmani_nbfcsud(a,r,k,n).

How to call the nondiagonal versions?

Perhaps just using the suffix "nd".

Perhaps after the (possible) "i".

DONE hindman2gen_fcs(a,n) is for hindmani_2^a(2).

This function should be called hindmani_r2k2_ofcs(a,n).

And also hindman_r2k2_ofcs(a,n) is needed.

There is also the nondiagonal versions, using a parameter tuple [k1,k2].

Again, just using suffix "nd".

So the functions should be called hindmannd_r2_fcs(a,k1,k2,n) and hindmanind_r2_fcs(a,k1,k2,n).
 Todo:
 The notion of a "Hindman parameter tuple"

As we have it currently for vanderWaerden numbers (see vanderwaerden_p in ComputerAlgebra/RamseyTheory/Lisp/VanderWaerden/Numbers.mac), we need the notion of a "Hindman parameter tuple".

Actually, we should centralise all such notions; likely in module ComputerAlgebra/RamseyTheory.

A "Hindman parameter tuple" should be a list [a,L], where a is a natural number >= 1, and L is a list of natural numbers >= 1, sorted in ascending order; but see below.

The parameter a (changing the starting number of the list of vertices) could, of course, be used also for vdWproblems etc.

Do we need a general scheme?

For the Hindmanproblems perhaps the special motivation to consider this additional parameter was to get a handle on the otherwise too big numbers?

So here we have special (historical) reasons to include parameter a.

But for a general systematic exploration of the field of Ramsey theory likely this variation should also be applied to vdWproblems etc.

Perhaps then those should be called tuples should be called "extended". And then we should also have Hindman parameter tuples L, and extended Hindman parameter tuples [a,L].
 Todo:
 Write tests
Definition in file HindmanProblems.hpp.