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The Stanley-Féray-Śniady formula for the generalized characters of the symmetric group

Fabio Scarabotti — 2011

Colloquium Mathematicae

We show that the explicit formula of Stanley-Féray-Śniady for the characters of the symmetric group has a natural extension to the generalized characters. These are the spherical functions of the unbalanced Gel’fand pair $(S ₙ \times S_{n - 1}, d i a g S_{n - 1})$ .

Amenable groups and cellular automata

Tullio G. Ceccherini-Silberstein; Antonio Machi; Fabio Scarabotti — 1999

Annales de l'institut Fourier

We show that the theorems of Moore and Myhill hold for cellular automata whose universes are Cayley graphs of amenable finitely generated groups. This extends the analogous result of A. Machi and F. Mignosi “Garden of Eden configurations for cellular automata on Cayley graphs of groups” for groups of sub-exponential growth.

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