General Mathematics

    

Abridgment of Cycles in GCS

Authors: Pierre Lamothe

A shortened English version of new concepts appeared this year in three French papers about cycles in Generalized Collatz Subsequences (GCS) and few new developments. Reduced and compact subseqs – Shape vector and shape rank – Triplet operator as a powerful tool to compose linear functions – Monoid of transition functions between elements of compact sequences – Diophantine equation pmx - rdy - q = 0 related to each monoid element – Shape class as general solution of this diophantine equation – Specific cyclic solution – Universal rotation function on q parameters – Condition for tranfer cyclic property to numbers – Cardinality of equation classes – Cycle occurence probability in classes – Layers of linked algebraic cycles.

Comments: 13 Pages.

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Submission history

[v1] 2020-12-26 23:06:57

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