2006/05/12 by A. V. Razumov, Yu. G. Stroganov
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics #Enumeration #Mathematical analysis #Mathematics #Physics #Sign (mathematics) #cond-mat.other #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1088/1742-5468/2006/07/p07004
published as J. Stat. Mech. (2006) P07004 · LaTeX 2e, 12 pages, minor corrections, references added
arxiv created 2006/05/12 · openalex publication_date 2006/07/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The properties of the most probable ground state candidate for the XXZ spin chain with the anisotropy parameter equal to −1/2 and an odd number of sites is considered. Some linear combinations of the components of the state considered, divided by the maximal component, coincide with the elementary symmetric polynomials in the corresponding Bethe roots. It is proved that these polynomials are equal to the numbers providing the refined enumeration of the alternating-sign matrices of order M +1 divided by the total number of the alternating-sign matrices of order M , for the chain of length 2 M +1.