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Olivier P. R. GERARD
Feel free to contact me through this wiki (Talk page, email-relay) about anything here.
French translation of main, information and help pages
in progress here
Waiting for the stabilization of the original english pages.
- Combinatorics, keen on permutations, words and integer partitions.
- Non classical algebras (non-associative systems, quasigroups, near rings and fields,
semigroups, matrices of continuous rank, ...)
- Special functions and their relations to combinatorics and quantum mechanics
- Rational generating functions and series expansions
- French versions of some pages and of some sequences
- Automatization of sequence formatting (with Eric Weisstein)
- Automatization of sequence transforms
- Batches of grid, scales and references sequences
- Mathematica parts of superseeker
- A few Mathematica code for sequences
You can write to me in
- French, English, German
Themes (In Progress)
Thematic table of a few sequences
|Theme||Sample Sequences||OEIS Link|
|Non group-theoretic structure of Bi-algebras||Number of nondecreasing sequences which are differences of two permutations of 1,2,...,n.||A019589|
|Special Functions||An hypergeometric interpretation of a simple binomial sum||A137644|
|Combinatorics of hierarchical structures||Hierarchical partitions of a set of n elements into two second level classes||A000558|
triangle of restricted ternary words by total length A137278
Open problem (Invitation):
Given an integer N>0, and after been found all the first N! terms of A217626, you were asked find either a function or algorithm which counts the number of different "trivial" palindromic patterns that could be built from these terms.
[1,9,2,9,1] is a "trivial" palindromic pattern.
[2,18,4,18,2] is not trivial, until it is re-written it as: [2,2*9,4,9*2,2]
So the "triviality" of such kind of patterns depends on the prime factorization of their components. Such behavior can not be reproduced by the prime numbers.
I can not spot it yet "the how", but the study of this matter might have deep implications in the number theory. (These patterns teach us how to build odd numbers in a similar way as what described by the Goldbach's Conjecture for the even numbers).
If you decide to face this friendly challenge,
Sincerely, with regards:
R. J. Cano 18:56, 15 December 2012 (UTC)