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A graph-theoretic proof of Cramer's rule | ||
Communications in Combinatorics and Optimization | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 مرداد 1404 اصل مقاله (335.22 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2025.30706.2586 | ||
نویسنده | ||
Sudip Bera* | ||
Faculty of Mathematics, Dhirubhai Ambani University, Gandhinagar-382007, India | ||
چکیده | ||
This note contains a new combinatorial proof of Cramer’s rule based on the Gessel-Viennot-Lindström Lemma. | ||
کلیدواژهها | ||
Cramer’s rule؛ combinatorial proof؛ determinants؛ digraphs | ||
مراجع | ||
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[6] G. Cramer, Introduction `a l’analyse des lignes courbes alg´ebriques, Chez les frères Cramer et C. Philibert, 1750.
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[8] C.G.J. Jacobi, De formatione et proprietatibus determinatium., J. fur Reine Angew. Math. 1841 (1841), no. 22, 285–318. https://doi.org/10.1515/crll.1841.22.285 [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. https://doi.org/10.1006/jcta.1996.0046 [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). | ||
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