A graph-theoretic proof of Cramer's rule

Articles in Press

Document Type : Original paper

Author

Faculty of Mathematics, Dhirubhai Ambani University, Gandhinagar-382007, India

Abstract

This note contains a new combinatorial proof of Cramer’s rule based on
the Gessel-Viennot-Lindström Lemma.

Keywords

Main Subjects

References

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https://doi.org/10.2307/2299943
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[9] O. Knill, Cauchy–Binet for pseudo-determinants, Linear Algebra Appl. 459 (2014), 522–547. https://doi.org/10.1016/j.laa.2014.07.013
[10] T. Muir, The Theory of Determinants in the Historical Order of Development, vol. 1, Macmillan and Company, limited, 1906.
[11] R.P. Stanley, A matrix for counting paths in acyclic digraphs, J. Comb. Theory, Ser. A. 74 (1996), no. 1, 169–172.
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[12] A-T. Vandermonde, Mémoire sur I’élimination, Hist. de l’Acad. Roy. des Sciences, Paris, 1772.
[13] D. Zeilberger, A combinatorial proof of Cramer’s rule, arXiv:2408.10282 [math.CO] (2024).
Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 04 August 2025

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