The Limit Distribution of a Number Theoretic Function Arising from a Problem in Statistical Mechanics Original Research Article

Letimage and for nset membership, variantimage, let Φ(n) be the number of matrices C which are products of Aʹs and Bʹs where both A and B must occur, such that the trace tr(C)=n. It has been conjectured thatimageThis conjecture is disproved by showing thatimagehas an absolutely continuous limit distribution with respect to the Lebesque measure.