Fermionic partition functions for a periodic soliton cellular automaton

Abstract

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 $\Delta =\infty$.

24 pages

References in corpus (5)

• Fundamental Cycle of a Periodic Box-Ball System
• Bethe ansatz and inverse scattering transform in a periodic box-ball system
• Inverse scattering method for a soliton cellular automaton
• On the initial value problem of a periodic box-ball system
• Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations

Cited by in corpus (1)

• Commuting Time Evolutions in the Tropical Periodic Toda Lattice