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Snake graphs, perfect matchings and continued fractions

Instantanés de recherche mathématique à Oberwolfach

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.

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Sujet mathématique

Algèbre et théorie des nombres
Mathématiques discrètes et fondements des mathématiques

Auteur(s)

Ralf Schiffler

Licence

DOI

10.14760/SNAP-2019-001-EN

Télécharger PDF

snapshot-2019-001.pdf

PDF

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      Sujet mathématique

      Algèbre et théorie des nombres
      Analyse
      Pédagogie et éducation
      Mathématiques discrètes et fondements des mathématiques
      Géométrie et Topologie
      Calcul numérique et calcul scientifique
      Théorie des probabilités et statistique

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      Chimie et sciences de la terre
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