Fermionic partition functions for a periodic soliton cellular automaton

Details Fermionic partition functions for a periodic soliton cellular automaton Fermionic partition functions for a periodic soliton cellular automaton

2010-11-30

arxiv.org/abs/1011.6426v1

J. Phys. A: Math. Theor. 44 (2011) 135204

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pages

Scientific paper

10.1088/1751-8113/44/13/135204

Fermionic formulas in combinatorial Bethe ansatz consist of sums of products of q-binomial coefficients. There exist refinements without a sum that are known to yield partition functions of box-ball systems with a prescribed soliton content. In this paper, such a refined fermionic formula is extended to the periodic box-ball system and a q-analogue of the Bethe root counting formula for XXZ chain at $\Delta=\infty$.

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