Friday, March 20, 2015

The Forking

Filed under: General — m759 @ 10:02 PM


An article in the new April issue of Notices of the American
Mathmatical Society 
suggests a search for connections
between the Calkin-Wilf tree and the modular group.

The search yields, for instance (in chronological order)

"Cutting sequences for geodesic flow on the modular surface
and continued fractions
," David J. Grahinet, Jeffrey C. Lagaria,
arXiv, 2 April 2001

"Orderings of the rationals and dynamical systems,"
Claudio Bonanno, Stefano Isola, arXiv, 14 May 2008.

"Periods of negative-regular continued fractions. Rational numbers."
Sergey Khrushchev and Michael Tyaglov, slides PDF, 11 Sept. 2012

"The Minkowski ?(x) function, a class of singular measures,
theta-constants, and mean-modular forms
," Giedrius Alkauskas,
arXiv, 20 Sept. 2012

"Forests of complex numbers,"
Melvyn B. Nathanson, arXiv, 1 Dec. 2014

Update of March 21, 2015:

For many more related papers, search by combining the
phrase "modular group" with phrases denoting forking structures
other than Calkin-Wilf, such as "cubic tree," "Stern-Brocot tree,"
and "Farey tree" (or "Farey sequence" or "Farey series" or
"Farey graph" ).

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