Publications
Mathematical publications and formalizations by Christopher Yamba, with preserved editions and interactive experiments.
From a Failed Corner Slide to a Verified Tableau Injection · technical article
Christopher Yamba — 23 October 2026, PDF edition, 11 pages.
A constructive positivity proof in height two, with exact obstructions and a Lean-checked coloring formula. The article explains counterexamples to proposed constructions and the completed Lean formalization for every finite alphabet. The height-two theorem and tableau injection are established work of Soojin Cho and JiSun Huh; this article does not claim a new solution of an unsolved problem.
Full illustrated article (PDF) · Recreational companion · Lean theorem · LaTeX source · PDF record
Author-published technical article; not externally peer reviewed.
Four diagonals suffice: completeness of Parikh matrices when letters occur at most twice · preprint
Christopher Yamba — 23 October 2026, version 1.
If every letter other than the first and the last occurs at most twice, the first four diagonals determine the Parikh matrix, with explicit formulas (a rectangle rule and a crossing chain). This extends the completeness theorem of the 2006 thesis. A sharpness family has ballot and Catalan numbers as its counts, and a conjecture covers higher multiplicities. The main theorem is formalised in Lean 4.
Article and abstract · PDF · LaTeX source · Verification package · Repository
Author-published research preprint; not peer reviewed.
From Euler numbers to the golden ratio: rigidity, ranges and the most ambiguous Parikh matrices for words with repeated letters · preprint
Christopher Yamba — 23 October 2026, version 1.
Which Parikh matrices determine their words, which values their entries can take, and which matrices are shared by the most words, for words with repeated letters. The answers run from Euler numbers to a golden-ratio threshold. The paper has 55 pages, eight figures, written proofs and Python checks of every computational statement.
Article and abstract · PDF · LaTeX source · Verification package · Repository
Author-published research preprint; not peer reviewed.
Partition stabilization and semigroup gaps for ternary Parikh matrices · preprint
Christopher Yamba — 19 October 2026, version 1.
Exact counting formulas for words with repeated letters, connecting ternary Parikh matrices to integer partitions and numerical-semigroup gaps. The paper determines specified matrix-class sizes, boundary corrections and attainable scattered-triple counts. It includes complete written proofs, three figures, computational checks and a partial Lean 4 certificate.
Article and abstract · PDF · LaTeX source · Verification package
Author-published research preprint; not peer reviewed.
The Ouroboros Problem · draft
Circular reasoning, predictive value and agentic AI for science — October 2026.
An illustrated essay on why a check that cannot fail carries no evidence. It follows the same loop from logic, where a circular proof is a null result, through statistics, where it becomes data leakage and double dipping, to agentic AI systems, where it can hide in seven places. It closes with design rules and a ten-question audit for agents that cannot cheat.
Read the essay · PDF edition · Print edition (PDF)
This is an author-published draft, written in collaboration with AI.
Counting Melodies · revision 2
Generating Functions, Regular Languages, and the Combinatorics of Pitch, Duration, and Silence — September 2026.
The revised manuscript connects a musical counting problem to integer compositions, regular languages, and generating functions. This edition adds engraved scores, ribbon and Young/Ferrers diagrams, and the complete catalogue of 32 rhythms of a 3/8 bar.
Read Counting Melodies v2 · Explore the rhythm and shape lab · Explore exact melody counts
This is an author-published draft. Its attribution, novelty qualifications, and incomplete formalization are recorded in the manuscript. The interactive experiments are separate companions to the text.
Earlier works · original editions
Combinatorial Mathematical Music Theory (2005) explores musical sets and mappings, multiset permutations, descent statistics, Parikh matrices, and q-analogues. The original Word manuscript is preserved as revision 1, with a separately labelled reading copy.
Parikh Matrices and Permutation Statistics (2006) is my mathematics degree thesis at Stockholm University, report No. 8. The supplied PDF is preserved as revision 1.
These earlier works have not been revised. Future corrections or developments will receive their own editions.