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The palette numbers of 2-bridge knots

Takuji Nakamura

Department of Engineering Science, Osaka Electro-Communication University, Hatsu-cho 18-8, Neyagawa, 572-8530, Japan

E-mail Address: n-takuji@osakac.ac.jp

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Yasutaka Nakanishi

Department of Mathematics, Kobe University, Rokkodai-cho 1-1, Nada-ku, Kobe 657-8501, Japan

E-mail Address: nakanisi@math.kobe-u.ac.jp

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Masahico Saito

Department of Mathematics, University of South Florida, Tampa, Florida 33620, USA

E-mail Address: saito@math.usf.edu

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, and

Shin Satoh

Department of Mathematics, Kobe University, Rokkodai-cho 1-1, Nada-ku, Kobe 657-8501, Japan

E-mail Address: shin@math.kobe-u.ac.jp

Corresponding author.

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https://doi.org/10.1142/S021821651750047XCited by:1 (Source: Crossref)

Abstract

We prove that for any odd $n \geq 3$ , the $n$ -palette number of any effectively $n$ -colorable $2$ -bridge knot is equal to $2 + ⌊ {log}_{2} n ⌋$ . Namely, there is an effectively $n$ -colored diagram of the $2$ -bridge knot such that the number of distinct colors that appeared in the diagram is exactly equal to $2 + ⌊ {log}_{2} n ⌋$ .

Keywords:

AMSC: 57M25, 57Q45

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