A New Multidimensional Slow Continued Fraction Algorithm and Stepped Surface

作者：Furukado Maki^*; Ito Shunji; Saito Asaki; Tamura Jun ichi; Yasutomi Shin ichi

来源：Experimental Mathematics, 2014, 23(4): 390-410.

DOI：10.1080/10586458.2014.917597

• continued fraction
• Farey map
• stepped surface
• multi-dimensional continued fraction algorithm
• Pisot number
• sturmian sequence
• real cubic number field
• tiling

We give a new algorithm of slow continued fraction expansion related to an arbitrary real cubic number field as a 2-dimensional version of the Farey map. Using our algorithm, we can find the generators of dual substitutions (so-called tiling substitutions) for any stepped surface for any cubic direction.

• 出版日期2014