Cauchy–Binet determinantal identity and enumeration of plane partitions in a high box
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 25-38 Cet article a éte moissonné depuis la source Math-Net.Ru

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The amplitudes of the leading asymptotics of the $XX0$ Heisenberg spin chain depend on the generating function of plane partitions with the additional conditions. In our paper we apply the Cauchy–Binet determinantal identity for derivation of the generating function of plane partitions with the fixed conjugate trace in a high box.
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N. M. Bogoliubov; C. L. Malyshev. Cauchy–Binet determinantal identity and enumeration of plane partitions in a high box. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 25-38. http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a1/

[1] N. M. Bogoliubov, “$XX$ Heisenberg chain and random walks”, J. Math. Sci., 138 (2006), 5636 | DOI | MR

[2] N. M. Bogoliubov, C. Malyshev, “Correlation functions of $XX0$ Heisenberg chain, $q$-binomial determinants, and random walks”, Nucl. Phys. B, 879 (2014), 268 | DOI | Zbl

[3] N. M. Bogoliubov, C. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70 (2015), 789 | DOI | MR | Zbl

[4] I. Macdonald, Symmetric Functions and Hall Polynomials, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995

[5] D. M. Bressoud, Proofs and Confirmations. The Story of the Alternating Sign Matrix Conjecture, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1999 | Zbl

[6] R. P. Stanley, Enumerative Combinatorics, Cambridge Studies in Advanced Mathematics, 2, Cambridge University Press, Cambridge, 1999 | Zbl

[7] N. M. Bogoliubov, C. Malyshev, “The phase model and the norm-trace generating function of plane partitions”, J. Stat. Mech., 2018 (2018), 083101 | DOI | MR | Zbl

[8] N. M. Bogoliubov, C. Malyshev, “The partition function of the four-vertex model in inhomogeneous external field and trace statistics”, J. Phys. A: Math. Theor., 52 (2019), 495002 | DOI | MR

[9] C. Malyshev, N. M. Bogoliubov, Heisenberg $XX$ chain, non-homogeneously parameterised generating exponential, and diagonally restricted plane partitions, arXiv: 2011.05148

[10] R. P. Stanley, “The conjugate trace and trace of a plane partition”, J. Comb. Theor. A, 14 (1973), 53 | DOI | Zbl

[11] E. Gansner, “The enumeration of plane partitions via the Burge correspondence”, Illinois J. Math., 25 (1981), 533 | DOI | MR | Zbl

[12] W. Fulton, Young Tableaux. With Applications to Representation Theory and Geometry, London Math. Soc. Stud. Texts, 35, Cambridge Univ. Press, Cambridge, 1997 | Zbl

[13] K. Klimyk, K. Schmudgen, Quantum Groups and their Representations, Springer-Verlag, Berlin, 1997 | Zbl

[14] A. J. Guttmann, A. L. Owczarek, X. G. Viennot, “Vicious walkers and Young tableaux I: Without walls”, J. Phys. A: Math. Gen., 31 (1998), 8123 | DOI | Zbl

[15] C. Krattenthaler, A. L. Guttmann, X. G. Viennot, “Vicious walkers, friendly walkers and Young tableaux: II. With a wall”, J. Phys. A: Math. Gen., 33 (2000), 8835 | DOI | Zbl