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Snake graphs, perfect matchings and continued fractions

Snapshots of modern mathematics from 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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Mathematical subjects

Algebra and Number Theory
Discrete Mathematics and Foundations

Author(s)

Ralf Schiffler

License

DOI (Digital Object Identifier)

10.14760/SNAP-2019-001-EN

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snapshot-2019-001.pdf

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