D. Knuth, Overlapping Pfa#ans, Electron. J. Combin. 3 (2) ("The Foata Festschrift") (1996), 151--163.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... j , H j (t) t = 1 t) and G i (t) such that G i (t = 1 t) 1 t) Gammak for a fixed k (such a choice does indeed exist; see [61, proof of Cor. 2.2] in Lemma 19. This yields k i j Gamma k i j Another point of view, beautifully set forth in [79], is that Pfaffians are more fundamental than determinants, in the sense that determinants are merely the bipartite special case of a general sum over matchings. Thus, out of the validity of (3.30) this enables to establish the validity of (3.32) and even of (3.33) by choosing F j (t) and H ....

D. E. Knuth, Overlapping pfaffians, Electron. J. Combin. 3 (no. 2, "The Foata Festschrift") (1996), paper #R5, 13 pp. (p. 11, 24)

....k (such a choice does indeed exist; see [61, proof of Cor. 2.2] in Lemma 19. This yields det 0i;jn Gamma1 k i j 2i Gamma j Gamma k i j 2i Gamma j = det 0i;jn Gamma1 2 i j 2i Gamma j : 9 Another point of view, beautifully set forth in [79], is that Pfaffians are more fundamental than determinants, in the sense that determinants are merely the bipartite special case of a general sum over matchings. ADVANCED DETERMINANT CALCULUS 25 Thus, out of the validity of (3.30) this enables to establish the validity of (3.32) and even of ....

D. E. Knuth, Overlapping pfaffians, Electron. J. Combin. 3 (no. 2, "The Foata Festschrift") (1996), paper #R5, 13 pp. (p. 11, 24)

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D. Knuth, Overlapping Pfa#ans, Electron. J. Combin. 3 (2) ("The Foata Festschrift") (1996), 151--163.

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