Vector Partition Identities for $2$D, $3$D and $n$D Lattices
Combinatorics
2023-02-03 v1
Abstract
We prove identities generating higher dimensional vector partitions. We derive theorems for integer lattice points in the 2D first quadrant, then generalize the approach to find 3D and -space lattice point vector region extensions. We also state combinatorial identities for Visible Point Vectors in 2D up to 5D and D first hyperquadrant and hyperpyramid lattices. 2D and 3D theorems for vector partitions with binary components are also derived.
Cite
@article{arxiv.2302.01091,
title = {Vector Partition Identities for $2$D, $3$D and $n$D Lattices},
author = {Geoffrey B. Campbell},
journal= {arXiv preprint arXiv:2302.01091},
year = {2023}
}
Comments
97 pages, 3 figures, to be submitted as several chapters to be published in the book "Vector Partitions Visible Points and Ramanujan Functions" (Taylor & Francis 2023)