A thread through time.
Mathematical ideas, preserved in their original editions. Follow the path from combinatorial music theory and permutation statistics to Counting Melodies.
The beauty of cancellation
A visual journey from a three-bead coloring puzzle to the Lean-checked height-two theorem of Cho and Huh.
Partition stabilization and semigroup gaps for ternary Parikh matrices
Exact counting formulas for words with repeated letters, connecting ternary Parikh matrices to integer partitions and numerical-semigroup gaps.
Read the paper, proofs and diagrams →The Symmetry Architecture of Merkurius
A piano piece from 1996, read as mathematics: a 44-bar meter palindrome, motifs answered by inversion and retrograde, and whole-tone harmony from augmented triads, with Burnside counts of the design space.
Read the article →Purple Square Atlas
Six geometric tiles, 1,296 arrangements, and 336 rotation classes. A visual application of Burnside’s lemma, with a LaTeX article, pattern explorer, and Lean cycle-model proof.
Read the article and the next step toward music →Current focus
Counting Melodies
Generating functions, regular languages, and the combinatorics of pitch, duration, and silence.
A melody.
A ribbon.
A new perspective.
Navigate Young and Ferrers diagrams, hear the rhythms, and solve a shape puzzle. All 32 rhythms of a 3/8 bar are waiting.
Explore the diagrams →Earlier works
Combinatorial Mathematical Music Theory
An early programme connecting musical sets and mappings, multiset permutations, descent statistics, Parikh matrices, and q-analogues.
Read original edition →Parikh Matrices and Permutation Statistics
The original mathematics degree thesis on Parikh matrix statistics, permutation statistics, and their relationship with descent statistics.
Read original edition →An independent author archive. Counting Melodies is an author-published draft. Earlier works are historical originals, not revised editions. Each release preserves its source files and checksums; the interactive experiments are separate companions.