@article{DA_2024_31_2_a3,
author = {D. B. Efimov},
title = {Enumeration of even and odd chord diagrams},
journal = {Diskretnyj analiz i issledovanie operacij},
pages = {63--79},
year = {2024},
volume = {31},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DA_2024_31_2_a3/}
}
D. B. Efimov. Enumeration of even and odd chord diagrams. Diskretnyj analiz i issledovanie operacij, Tome 31 (2024) no. 2, pp. 63-79. http://geodesic.mathdoc.fr/item/DA_2024_31_2_a3/
[1] Acan H., An enumerative-probabilistic study of chord diagrams, PhD Thes., Ohio State Univ., Columbus, 2013, 144 pp. | MR
[2] E. S. Krasko, I. N. Labutin, and A. V. Omelchenko, “Enumeration of labelled and unlabelled Hamiltonian cycles in complete $k$-partite graphs”, Zap. Nauchn. Semin. POMI, 488, 2019, 119–142 (Russian)
[3] Nakamigawa T., “The expansion of a chord diagram and the Genocchi numbers”, Ars Math. Contemp., 18 (2020), 381–391 | DOI | MR | Zbl
[4] Sullivan E., “Linear chord diagrams with long chords”, Electron. J. Comb., 24:4 (2017), P4.20, 8 pp. | MR
[5] Cameron N. T., Killpatrick K., “Statistics on linear chord diagrams”, Discrete Math. Theor. Comput. Sci., 21:2 (2020), 11, 10 pp. | MR
[6] Acan H., “On a uniformly random chord diagram and its intersection graph”, Discrete Math., 340:8 (2017), 1967–1985 | DOI | MR | Zbl
[7] Touchard J., “Sur un problème de configurations et sur les fractions continues”, Canad. J. Math., 4 (1952), 2–25 (French) | DOI | MR | Zbl
[8] Riordan J., “The distribution of crossing of chords joining pairs of $2n$ points on a circle”, Math. Comput., 29:129 (1975), 215–222 | MR | Zbl
[9] Courtiel J., Yeats K., Zeilberger N., “Connected chord diagrams and bridgeless maps”, Electron. J. Comb., 26:4 (2019), P4.37, 56 pp. | MR | Zbl
[10] Mahmoud A. A., Yeats K., “Connected chord diagrams and the combinatorics of asymptotic expansions”, J. Integer Seq., 25:7 (2022), 22.7.5, 22 pp. | MR | Zbl
[11] Shevelev V. S., “Combinatorial minors for matrix functions and their applications”, Zesz. Nauk. Politech. Śląsk. Ser. Mat. Stosow, 2014, no. 4, 5–16 | MR
[12] V. S. Shevelev, “Some problems of the theory of enumerating the permutations with restricted positions”, J. Sov. Math., 61:4 (1992), 2272–2317 | DOI | MR | Zbl
[13] H. Minc, Permanents, Addison-Wesley, Reading, MA, 1978 | MR | MR | Zbl
[14] Stembridge J. R., “Nonintersecting paths, Pfaffians, and plane partitions”, Adv. Math., 83 (1990), 96–131 | DOI | MR
[15] Barvinok A., Combinatorics and complexity of partition functions, Algorithms Comb., 30, Springer, Cham, 2016, 304 pp. | MR | Zbl
[16] Fishel S., Grojnowski I., “Canonical bases for the Brauer centralizer algebra”, Math. Res. Lett., 2 (1995), 15–26 | DOI | MR | Zbl
[17] Barcelo H., Ram A., “Combinatorial representation theory”, New perspectives in algebraic combinatorics, Math. Sci. Res. Inst. Publ., 38, Camb. Univ. Press, New York, 1999, 23–90 | MR | Zbl
[18] Shalile A., “On the center of the Brauer algebra”, Algebr. Represent. Theory, 16 (2013), 65–100 | DOI | MR | Zbl
[19] Schwartz M., “Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices”, Linear Algebra Appl., 430 (2009), 1364–1374 | DOI | MR | Zbl
[20] L. Lovász and M. D. Plummer, Matching Theory, North-Holland, Amsterdam, 1986 | MR | Zbl
[21] Gabiati G., Maffioli F., “On the computation of Pfaffians”, Discrete Appl. Math., 51 (1994), 269–275 | DOI | MR
[22] Wimmer M., “Algorithm 923: Efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices”, ACM Trans. Math. Softw., 38:4 (2012), 30, 17 pp. | DOI | MR | Zbl
[23] The on-line encyclopedia of integer sequences, , OEIS Found., Highland Park, NJ, 2024 (accessed Mar. 3, 2024) oeis.org