A note on the determinant of a Toeplitz-Hessenberg matrix

• Autorzy: Mircea Merca
• Języki publikacji: EN

Abstrakty

EN

The nth-order determinant of a Toeplitz-Hessenberg matrix is expressed as a sum over the integer partitions of n. Many combinatorial identities involving integer partitions and multinomial coefficients can be generated using this formula.

Słowa kluczowe

EN

Toeplitz-Hessenberg matrix; integer partition; multinomial coefficient

Kategorie tematyczne

• 05A19: Combinatorial identities, bijective combinatorics
• 15A15: Determinants, permanents, other special matrix functions
• 05A17: Partitions of integers

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2013
• Tom: 1
• Strony: 10-16

Daty

otrzymano

2013-08-07

zaakceptowano

2013-08-09

online

2013-10-02

Twórcy

autor

Mircea Merca

• Department of Mathematics, University of Craiova, 200585 Craiova,
  Romania

Bibliografia

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• [3] J. M. Bogoya, A. Böttcher, S. M. Grudsky, E. A. Maksimenko, Eigenvectors of Hessenberg Toeplitz matrices and a problem by Dai, Geary, and Kadanoff, Linear Algebra Appl. 436 (2012), 3480–3492. [WoS]
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• [5] X. W. Chang, M. J. Gander, S. Karaa, Asymptotic properties of the QR factorization of banded Hessenberg–Toeplitz matrices. Numer. Linear Algebra Appl. 12 (2005), 659–682.
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• [8] R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics. Addison-Wesley, New York, 1994.
• [9] A. Inselberg, On determinants of Toeplitz-Hessenberg matrices arising in power series, J. Math. Anal. Appl. 63 (1978), 347–353. [Crossref]
• [10] A. J. E. M. Janssen, Asymptotics of the Perron-Frobenius eigenvalue of nonnegative Hessenberg-Toeplitz matrices, IEEE Trans. Inf. Theor., 35 (1989), 1340–1344.
• [11] I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd ed., Clarendon Press, Oxford, 1995.
• [12] P. A. MacMahon, Combinatory analysis. Two volumes (bound as one), Chelsea Publishing Co., New York, 1960.
• [13] P. Mongelli, Combinatorial interpretations of particular evaluations of complete and elementary symmetric functions, Electron. J. Combin. 19 (2012), paper 12, 23 pp.
• [14] T. Muir, The theory of determinants in the historical order of development. Four volumes, Dover Publications, New York, 1960.
• [15] R. Van Malderen, Non-recursive expressions for even-index Bernoulli numbers: A remarkable sequence of determinants, arXiv:math/0505437v1, 2005.

Identyfikatory

DOI

10.2478/spma-2013-0003