Geodesic
Random ordered lattice paths generated by operators satisfying the Cuntz algebra
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 80-90

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The technique based on operators satisfying the Cuntz algebra is used for the enumeration of Dyck, Motzkin and Łukasiewicz lattice paths. It is shown that the weighted paths may be considered as the generators of master fields of the quantum field theory. 
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     author = {N. M. Bogoliubov},
     title = {Random ordered lattice paths generated by operators satisfying the {Cuntz} algebra},
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N. M. Bogoliubov. Random ordered lattice paths generated by operators satisfying the Cuntz algebra. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 80-90. http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a2/