The paper considers the chainable index of a square matrix of order n and proves that it does not exceed n − 1. Also it is demonstrated that every integer in between 0 and n − 1 is a value of the chainable index.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yu. A. Al’pin and I. V. Bashkin, “Nonnegative chainable matrices”, Zap. Nauchn. Semin. POMI, 496, 5–25 (2020); English transl., J. Math. Sci., 255, No. 3, 217–230 (2021).
Yu. A. Al’pin and I. V. Bashkin, “Nonnegative chainable matrices and Kolmogorov’s condition”, Zap. Nauchn. Semin. POMI, 504, 5–20 (2021); English transl., J. Math. Sci., 262, No. 1, 1–10 (2022).
V. N. Sachkov and V. E. Tarakanov, Combinatorics of Nonnegative Matrices, Amer. Math. Soc. (2002).
D. J. Hartfiel and C. J. Maxson, “The chainable matrix, a special combinatorial matrix”, Discrete Math., 12, 245–256 (1975).
R. Sinkhorn and P. Knopp, “Problems involving diagonal products in nonnegative matrices”, Trans. Amer. Math. Soc., 136, 67–75 (1969).
H. Wielandt, “Unzerlegbare, nicht negative Matrizen”, Math. Zeit., 52, No. 1, 642–648 (1950).
Author information
Authors and Affiliations
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 514, 2022, pp. 5–17.
Translated by the authors.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Alpin, Y.A., Guterman, A.E. & Shafeev, E.R. An Upper Bound for the Chainable Index. J Math Sci 272, 487–495 (2023). https://doi.org/10.1007/s10958-023-06443-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06443-9