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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@article{ZNSL_2024_532_a2,
     author = {N. M. Bogoliubov},
     title = {Random ordered lattice paths generated by operators satisfying the {Cuntz} algebra},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {80--90},
     year = {2024},
     volume = {532},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a2/}
}
TY  - JOUR
AU  - N. M. Bogoliubov
TI  - Random ordered lattice paths generated by operators satisfying the Cuntz algebra
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2024
SP  - 80
EP  - 90
VL  - 532
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a2/
LA  - en
ID  - ZNSL_2024_532_a2
ER  - 
%0 Journal Article
%A N. M. Bogoliubov
%T Random ordered lattice paths generated by operators satisfying the Cuntz algebra
%J Zapiski Nauchnykh Seminarov POMI
%D 2024
%P 80-90
%V 532
%U http://geodesic.mathdoc.fr/item/ZNSL_2024_532_a2/
%G en
%F ZNSL_2024_532_a2
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/

[1] S. G. Mohanty, Lattice Path Counting and Applications, Academic Press, New York, 1979 | MR | Zbl

[2] E. Deutsch, “Dyck path enumeration”, Discrete Math., 204 (1999), 167–202 | DOI | MR | Zbl

[3] J-L. Baril, H. Prodinger, “Enumeration of Partial Łukasiewicz Paths”, ECA, 3:1 (2023), S2R2 | MR | Zbl

[4] Li Gan, S. Ouvry, A. Polychronakos, “Combinatorics of generalized Dyck and Motzkin paths”, Phys. Rev. E, 106 (2022), 044123 | DOI | MR

[5] T. Selig, H. Zhu, Parking functions and Łukasiewicz paths, 2024, arXiv: 2403.17438 | MR

[6] C. Banderier, M. Wallner, “Lattice paths with catastrophes”, Disc. Math. Theor. Comp. Sci., 19 (2017), 23 | MR | Zbl

[7] C. Krattenthaler, “Lattice path enumeration”, Handbook of enumerative combinatorics (Boca Raton), Discrete Math. Appl., CRC Press, Boca Raton, FL, 2015, 589–678 | MR | Zbl

[8] G. Cicuta, M. Contedini, L. Molinari, “Enumeration of simple random walks and tridiagonal matrices”, J. Math. Gen., 35 (2002), 1125–1146 | DOI | MR | Zbl

[9] C. Banderier, P. Flajolet, “Basic analytic combinatorics of directed lattice paths”, Theor. Comp. Sci., 281 (2002), 37–80 | DOI | MR | Zbl

[10] N. M. Bogoliubov, “Enumerative combinatorix of $XX0$ Heisenberg chain”, Zap. nauchn. semin. POMI, 487, 2019, 53–67 | MR

[11] R. Gopakumar, D. Gross, “Mastering the master field”, Nucl. Phys. B, 451 (1995), 379–415 | DOI | MR | Zbl

[12] M. R. Douglas, “Large N gauge theory – Expansions and transitions”, Nucl. Phys. B, 41 (1995), 66–91 | DOI | MR | Zbl

[13] D. V. Voiculescu, K. J. Dykema, A. Nica, Free Random Variables, CRM Monograph Series, 1, AMS, Providence, 1992 | DOI | MR | Zbl

[14] N. M. Bogoliubov, “Boxed plane partitions as an exactly solvable boson model”, J. Phys. A, 38 (2005), 9415–9430 | DOI | MR | Zbl

[15] V. Fock, “Konfigurationsraum und zwiete Quantelung”, Zs. f. Phys., 75 (1932), 622–647 | DOI | Zbl

[16] P. Carruthers, M. M. Nieto, “Phase and Angle Variables in Quantum Mechanics”, Rev. Mod. Phys., 40 (1968), 411–440 | DOI

[17] K. V. Brodovitsky, “On the $\int\limits_0^\pi\frac{\sin^mx}{p+q\cos x}~dx$ integral”, Dokl. Akad. Nauk SSSR, 120 (1958), 1178–1179 | MR