4 papers
math.CO2025
Computing the 4D Geode
Dean Rubine
The closed form for the hyper-Catalan number C[m2,m3,m4,...], which counts the number of subdivisions of a roofed polygon into m2 triangles, m3 quadrilaterals, m4 pentagons, etc.,…
math.CO2025
A New Proof of Fine's Identity using Wildberger's Polynomial Formula
Dean Rubine
In 1959, N. J. Fine showed that the sum of the multinomial coefficients corresponding to the partitions of a natural number into parts is a binomial coefficient: $$ \sum_{\…
math.CO2025
Finite Interpretation of the Hyper-Catalan Series Zero and its Powers
Dean Rubine, Pratham Mukewar
In 2025, Wildberger and Rubine showed the formal series zero of the univariate geometric polynomial is , the generating series for the hyper-Catalan numbers $\mathbf{C}…
math.CO2025
Hyper-Catalan and Geode Recurrences and Three Conjectures of Wildberger
Dean Rubine
The hyper-Catalan number counts the number of subdivisions of a roofed polygon into triangles, quadrilaterals, pentagons, etc. Its closed…