Computing vector partition functions

2023/02/14 by Milev, Todor
#05E10 #17B22 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2302.06894

Abstract

A vector partition function is the number of ways to write a vector as a non-negative integer-coefficient sum of the elements of a finite set of vectors Δ. We present a new algorithm for computing closed-form formulas for vector partition functions as quasi-polynomials over a finite set of pointed polyhedral cones, implemented in the ``calculator'' computer algebra system. We include an exposition of previously known theory of vector partition functions. While our results are not new, our exposition is elementary and self-contained.

Related

• Partial fraction decompositions and an algorithm for computing the vector partition function
• External columns and chambers of vector partition functions
• Vector partition function and representation theory
• Towards computing vector partition functions by iterated partial fraction decomposition
• An explicit formulation for two dimensional vector partition functions