English

Rectangle partitions generalizing integer partitions

Combinatorics 2025-10-02 v2 Number Theory

Abstract

In this paper, we introduce a natural geometric extension of the partition function. More precisely, we investigate the problem of counting partitions of a rectangle into rectangular blocks with integer sides. Here, two partitions of a rectangle are indistinguishable if they consist of the same multiset of blocks, their geometric arrangement does not matter.

Keywords

Cite

@article{arxiv.2509.20495,
  title  = {Rectangle partitions generalizing integer partitions},
  author = {Krystian Gajdzica and Robin Visser and Maciej Zakarczemny},
  journal= {arXiv preprint arXiv:2509.20495},
  year   = {2025}
}

Comments

23 Pages, 4 Figures, 2 Tables