Hiroshima Mathematical Journal

Generating functions of Box and Ball System

Mami Okiyoshi

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Abstract

Generating functions of Box and Ball System (BBS) are defined and studied. When the number of balls is finite, we show that the generating function is a rational function. When there are infinitely many balls, we conjecture that the generating function is rational if and only if the BBS is semi-periodic. We prove the conjecture in a special case. We also study the generating function of the BBS with a limited cart, including semi-periodic cases.

Article information

Source
Hiroshima Math. J., Volume 45, Number 2 (2015), 147-163.

Dates
First available in Project Euclid: 10 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1439219706

Digital Object Identifier
doi:10.32917/hmj/1439219706

Mathematical Reviews number (MathSciNet)
MR3379000

Zentralblatt MATH identifier
1325.26040

Subjects
Primary: 26C15: Rational functions [See also 14Pxx] 37K40: Soliton theory, asymptotic behavior of solutions

Keywords
Box and Ball System generating functions

Citation

Okiyoshi, Mami. Generating functions of Box and Ball System. Hiroshima Math. J. 45 (2015), no. 2, 147--163. doi:10.32917/hmj/1439219706. https://projecteuclid.org/euclid.hmj/1439219706


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