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Snake graphs, perfect matchings and continued fractions

Oberwolfach'tan

Snake graphs, perfect matchings and continued fractions

A continued fraction is a way of representing a real number by a sequence of integers. We present a new way to think about these continued fractions using snake graphs, which are sequences of squares in the plane. You start with one square, add another to the right or to the top, then another to the right or the top of the previous one, and so on. Each continued fraction corresponds to a snake graph and vice versa, via “perfect matchings” of the snake graph. We explain what this means and why a mathematician would call this a combinatorial realization of continued fractions.

If you are interested in translating this Snapshot, please contact us at info@imaginary.org

Matematiksel konular

Cebir ve Sayılar Kuramı
Ayrık Matematik ve Matematiğin Temelleri

Yazar(lar)

Ralf Schiffler

Lisans

DOI (Dijital nesne belirteci)

10.14760/SNAP-2019-001-EN

PDF indir

snapshot-2019-001.pdf

PDF

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      Matematiksel konular

      Cebir ve Sayılar Kuramı
      Analiz
      Eğitim ve Eğitim Bilimi
      Ayrık Matematik ve Matematiğin Temelleri
      Geometri ve Topoloji
      Nümerik ve Hesap Analizi
      Olasılık Kuramı ve İstatistik

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