Generalized O-sequences and Hilbert functions of points

Let D={d1,…,dr} be a list of positive integers. We generalize the standard binomial coefficients by putting for a b. We then generalize Macaulayʹs O-sequences and we refer to our sequences as OD-sequences. We recall the kD-configurations we constructed in [S. Sabourin, Generalized k-configurations, in preparation], which generalize both 0-dimensional reduced complete intersections and the k-configurations studied by Geramita, Harima, and Shin. We then use OD-sequences to characterize the Hilbert functions of kD-configurations.