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<p>In this paper, we introduce a&#xa0;natural geometric extension of the partition function. More precisely, we investigate the problem of counting partitions of a&#xa0;rectangle into rectangular blocks with integer sides. Here, two partitions of a&#xa0;rectangle are indistinguishable if they consist of the same multiset of blocks, their geometric arrangement does not matter.</p>

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Rectangle Partitions Generalizing Integer Partitions

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月28日

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  • Krystian Gajdzica,
  • Robin Visser,
  • Maciej Zakarczemny

摘要

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.