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CLASSIFICATION OF GENERALIZED PAPER FOLDING SEQUENCES

Yun, Junghee;Lim, Junhwi;Hahm, Nahmwoo

  • Received : 2013.05.22
  • Accepted : 2013.05.31
  • Published : 2013.09.25

Abstract

Generalized paper folding sequences $X^n_p$ and $(X_pY_q)^n$ where $X,Y{\in}\{R,L,U,D\}$, and $n,p,q{\in}\mathbb{N}$, and with $p,q{\geq}2$ are classified in this paper. We show that all generalized paper folding sequences $X^n_p$ are classified into one type if we classify generalize paper folding sequences along with the numbers of downwards and upwards. In addition, we investigate the numbers of downwards and upwards in $(X_pY_q)^n$ and prove that all generalized paper folding sequences $(X_pY_q)^n$ are classified into two types.

Keywords

classification;paper folding sequences;upward;downward

References

  1. Jean-Paul Allouche, The number of factors in a paperfolding sequence, Bull. Austral. Math. Soc. 46 (1992), 23-32. https://doi.org/10.1017/S0004972700011655
  2. Bruce Bates, Martin Bunder and Keith Tognetti, Mirroring and interleaving in the paperfolding sequence, App. Anal. Discrete Math. 4 (2010), 96-118. https://doi.org/10.2298/AADM1000005B
  3. Christiane Bercoff, A family of tag systems for paperfolding sequence, Lect. Notes Comput. Sc. 600 (1995), 303-312.
  4. Chandler Davis and Donald E. Knuth, Number representations and dragon curves, J. Rec. Math. 3 (1970), 66-81.
  5. Michel Dekking, Paperfolding, morphisms, planefilling, curves and fractal tiles, Theor. Comput. Sci. 414(1) (2012), 20-37 https://doi.org/10.1016/j.tcs.2011.09.025
  6. M. France and A. J. Poorten, Arithmetic and analytic properties of paper folding sequences, Bull. Austral. Math. Soc. 24(1981), 123-131. https://doi.org/10.1017/S0004972700007486
  7. Sung Gye Lee, Jin Soo Kim and Won Choi, Relation between folding and unfolding paper of rectangle and (0,1)-pattern, J. Korean Soc. Math. Ed. Ser. E, 23(3)(2009), 507-522.
  8. Junghee Yun and Nahmwoo Hahm, Counting problems in generalized paper folding sequences, Honam Math. J. 34(3) (2012), 423-438. https://doi.org/10.5831/HMJ.2012.34.3.423