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.
Citation
Mami Okiyoshi. "Generating functions of Box and Ball System." Hiroshima Math. J. 45 (2) 147 - 163, July 2015. https://doi.org/10.32917/hmj/1439219706
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