Lattice paths and the Prouhet-Thue-Morse sequence

Bing Gao; Shishuo Fu

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Lattice paths and the Prouhet-Thue-Morse sequence

Bing Gao,Shishuo Fu *

College of Mathematics and Statistics, Chongqing University, Huxi campus, Chongqing 401331

*Correspondence author

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Funding: ***Foundation （No.00000000）, *** Foundation （No.00000000）

Opened online:27 March 2023

Accepted by: none

Citation: Bing Gao,Shishuo Fu.Lattice paths and the Prouhet-Thue-Morse sequence[OL]. [27 March 2023] http://en.paper.edu.cn/en_releasepaper/content/4759531

Using Flajolet's combinatorial theory of continued fractions and axial symmetry of lattice paths, we show that the enumeration of certain lattice paths modulo two yields the ubiquitous Prouhet-Thue-Morse sequence. This answers an open problem of Berstel et al.

Keywords:Basic mathematics;Continuted fractions;Lattice paths;Prouhet-Thue-Morse sequence;Symmetry

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