# CLASSIFICATION OF GENERALIZED PAPER FOLDING SEQUENCES

Yun, Junghee;Lim, Junhwi;Hahm, Nahmwoo

• Accepted : 2013.05.31
• Published : 2013.09.25
• 32 11

#### 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

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