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arXiv · 2509.20495

Rectangle partitions generalizing integer partitions

Krystian Gajdzica·Robin Visser·Maciej Zakarczemny
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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.

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Krystian Gajdzica, Robin Visser, Maciej Zakarczemny. 2025-10-01. Rectangle partitions generalizing integer partitions. https://arxiv.org/abs/2509.20495

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