Symmetry, Combinatorics, Artificial Intelligence, Music and Spectroscopy

Symmetry forms the foundation of combinatorial theories and algorithms enumeration such as Möbius inversion, Euler totient functions, celebrated Pólya’s theory under symmetric group action. As machine learning artificial intelligence techniques play increasingly important roles in perception music to image processing that are central many disciplines, combinatorics, graph theory, symmetry act powerful bridges developments for varied applications. In this review, we bring together confluence spectroscopy two primary disciplines outline several interconnections development generation musical patterns east west a variety spectroscopic signatures molecules. Combinatorial conjunction with can be harnessed generate scales, intensity ESR spectra, multiple quantum NMR nuclear spin statistics both fermions bosons, colorings hyperplanes hypercubes, chiral isomers, vibrational modes complex systems including supergiant fullerenes, exemplified by our work on golden fullerene C150,000. shown yield construction chords scales called ragas exemplify patterns. We also applications Hadamard matrices magic squares balanced-pitch chords. Machine musical, spectroscopic, considered.