Lloyd, E. Keith Redfield’s proofs of MacMahon’s conjecture. (English) Zbl 0701.01005 Hist. Math. 17, No. 1, 36-47 (1990). In 1927 P. A. MacMahon published a conjecture concerning \(n\)-dimensional determinants (or permanents) of order \(p\). J. H. Redfield discovered two proofs of the conjecture. In 1927, in a letter to MacMahon he starts with two permutation groups \(G_ 1\) and \(G_ 2\) and describes a structure which is now called the wreath product of \(G_ 1[G_ 2]\) of the groups; but he does not give it a name, nor does he have a notation for the group itself. In 1940 Redfield submitted a second paper to the American Journal of Mathematics, but it was rejected; some 40 years after Redfield’s death, it was published in [J. H. Redfield, J. Graph Theory 8, 205–224 (1984; Zbl 0538.05003)]. The present author presents and discusses two proofs of the conjecture, based on unpublished, Redfield’s papers and letters. Reviewer: W.Wieslaw MSC: 01A60 History of mathematics in the 20th century 05-03 History of combinatorics 15A15 Determinants, permanents, traces, other special matrix functions Keywords:\(n\)-dimensional determinant; permanent; permutation groups; wreath product Biographic References: MacMahon, P. A.; Redfield, J. H. Citations:Zbl 0538.05003 PDFBibTeX XMLCite \textit{E. K. Lloyd}, Hist. Math. 17, No. 1, 36--47 (1990; Zbl 0701.01005) Full Text: DOI References: [1] Cock, F. J., Letter to J. H. Redfield, 9 April 1928 (1928) [2] Ledermann, W., Introduction to the theory of finite groups (1961), Oliver & Boyd: Oliver & Boyd Edinburgh · Zbl 0041.35901 [3] Littlewood, D. E.; Richardson, A. R., Group characters and algebra, Philosophical Transactions of the Royal Society of London Series A, 233, 99-141 (1934) · Zbl 0009.20203 [4] Lloyd, E. 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