论文信息 - Christoffel Words and the Calkin-Wilf Tree

Christoffel Words and the Calkin-Wilf Tree

In this note we present some results on the Calkin-Wilf tree of irreducible fractions, giving an insight on the duality relating it to the Stern-Brocot tree, and proving noncommutative versions of known results relating labels of the Calkin-Wilf trees to hyperbinary expansions of positive integers. The main tool is the Christoffel tree introduced in a paper by Berstel and de Luca.

Alessandro De Luca | Christophe Reutenauer

[1] Aldo de Luca,et al. Sturmian Words, Lyndon Words and Trees , 1997, Theor. Comput. Sci..

[2] B. M. Fulk. MATH , 1992 .

[3] M. Stern. Ueber eine zahlentheoretische Funktion. , 1858 .

[4] Aldo de Luca,et al. Involutions of epicentral words , 2010, Eur. J. Comb..

[5] Jeffrey Shallit,et al. The ring of k-regular sequences, II , 2003, Theor. Comput. Sci..

[6] Jeffrey Shallit,et al. The Ring of k-Regular Sequences , 1990, Theor. Comput. Sci..

[7] G. N. Raney. On continued fractions and finite automata , 1973 .

[8] C. Reutenauer,et al. Noncommutative Rational Series with Applications , 2010 .

[9] Martin Aigner,et al. Proofs from THE BOOK , 1998 .

[10] Aldo de Luca,et al. On an involution of Christoffel words and Sturmian morphisms , 2008, Eur. J. Comb..

[11] Herbert S. Wilf,et al. Recounting the Rationals , 2000, Am. Math. Mon..