Permutable polynomials for several variables

Summary The Russian mathematician P. L. Chebyshev defined and studied a class of polynomials of one variable. These polynomials have many in teresting properties including commutativity and closure with respect to composition. In this article we show how to generalize this property to several variables. Special attention is given to the case of three variables. Results concerning how to compute the polynomials, their value at certain points, closed forms, recurrence relations, and generating functions are presented.