Hafnian of some three-parameter Toeplitz matrices and perfect matchings of arc and chord diagrams
Автор: Efimov D.B.
Журнал: Известия Коми научного центра УрО РАН @izvestia-komisc
Статья в выпуске: 6 (52), 2021 года.
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We obtain an explicit formula for exact calculatingthe hafnian of 3-parameter Toeplitz matrices of aspecial type in polynomial time. We also give anasymptotic estimate for the hafnian of this type ofmatrices. Separately, we consider a case of non-negative integer parameters, when calculating the haf-nian is equivalent to enumerating perfect matchingsof arc and chord diagrams.
Hafnian, toeplitz matrix, perfect matching, arc diagram, chord diagram, bessel polynomial
Короткий адрес: https://sciup.org/149139334
IDR: 149139334 | DOI: 10.19110/1994-5655-2021-6-5-13
Список литературы Hafnian of some three-parameter Toeplitz matrices and perfect matchings of arc and chord diagrams
- Krasko E., Omelchenko A. Enumeration of chorddiagrams without loops and parallel chords //Electron. J.Combin. 2017. Vol. 24. Article3.43.
- Sullivan E. Linear chord diagrams with longchords // Electron. J.Combin. 2017. Vol. 24.Article 4.20.
- Efimov D.B. The hafnian and a commutativeanalogue of the Grassmann algebra // Electron.J. Linear Algebra. 2018. Vol. 34. P. 54-60.
- Efimov D.B. Gafnian teplitsevykh matrits spetsial'nogo vida, sovershennyye parosochetaniya ipolinomy Besselya [The hafnian of Toeplitz matrices of a special type, perfect matchings and Bessel polynomials] // Bull. of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2018. No. 3(28). P. 56-64. Available at https://arxiv.org/abs/1904.08651.Ефимов Д.Б. Гафниан теплицевых матриц специального вида, совершенные паросочетанияи полиномы Бесселя // Вестник Cыктывкарского университета. Серия 1: Математика.Механика. Информатика. 2018. № 3(28). С.56-64.
- Grosswald E. Bessel Polynomials. Springer,1978.
- Grosswald E. On some algebraic properties of theBessel polynomials //Trans. Amer. Math. Soc.1951. Vol. 71. P. 197-210.
- Sloane N.J.A. et al. The On-Line Encyclopediaof Integer Sequences. 2020. Available athttps://oeis.org/.
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