A Survey on Computational Aspects of Polynomial Amoebas

An Approach to Multidimensional Discrete Generating Series

“…An effective method of obtaining explicit formulas for the coefficients of a generating function related to the Aztec diamond and a generating function related to the permutations with cycles was derived in [8,9]. Using the notion of amoeba [10] of the characteristic polynomial of a difference equation, a description for the solution space of a multidimensional difference equation with constant coefficients was obtained in [11]. A generalization to several variables of the classical Poincaré theorem on the asymptotic behavior of solutions of a linear difference equation is presented in [12].…”