Periodicity of free subgroup numbers modulo prime powers

We completely characterise when the sequence of free subgroup numbers of a finitely generated virtually free group is ultimately periodic modulo a given prime power.Comment: AmS-LaTeX; 18 page

A note on higher-dimensional magic matrices

We provide exact and asymptotic formulae for the number of unrestricted, respectively indecomposable, $d$-dimensional matrices where the sum of all matrix entries with one coordinate fixed equals 2.Comment: AmS-LaTeX, 9 page