In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry { \it win-loss}. We present in this article another generalization (always associated with a sequence of positive numbers) that preserves the symmetry { \it win-loss}. This approach is also based on generating functions and presents constraints of non-negativeness, similar to those encountered in our previous articles.
Categories: math-ph cond-mat.stat-mech math.MP quant-ph