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<p>In this paper, we examine tessellations of a rectangle with tiles of two types and find the number of such tessellations by summing elements of Pascal’s pyramid. We consider two cases: tessellations of rectangles with square tiles of two sizes and tessellations of rectangles with smaller rectangular and square tiles of two different colors. We prove some combinatorial properties of ascending sections of the Pascal pyramid and present theorems about recurrent relations and explicit expressions for the number of tessellations in both cases through sums of elements of upward sections of the Pascal pyramid.</p>

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CALCULATION OF THE NUMBER OF TESSELLATIONS OF A RECTANGLE WITH TWO TYPES OF TILES

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • O. V. Kuzmin,
  • M. V. Strikhar

摘要

In this paper, we examine tessellations of a rectangle with tiles of two types and find the number of such tessellations by summing elements of Pascal’s pyramid. We consider two cases: tessellations of rectangles with square tiles of two sizes and tessellations of rectangles with smaller rectangular and square tiles of two different colors. We prove some combinatorial properties of ascending sections of the Pascal pyramid and present theorems about recurrent relations and explicit expressions for the number of tessellations in both cases through sums of elements of upward sections of the Pascal pyramid.