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On sums of determinants of intersection matrices of Petrie matricest

  • M. Gordon (a1) and W. T. Tutte (a1)

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A Petrie matrix (Kendall (1), (2)) is a matrix of O's and l's such that the l's in each column occur consecutively. An example follows.

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(1)Kendall, D. G.A statistical approach to Flinders Petrie–s sequence dating. Bull. Inst. Internat. Statist. 40 (1963), 657680.
(2)Kendall, D. G.A mathematical approach to seriation. Philos. Trans. Roy. Soc. Lond. Scr. A269 (1970), 125134.
(3)Fixman, M.Excluded volume in polymer chains. J. Chem. Phys. 23 (1955), 1656.
(4)Yamakawa, H.Modern theory of polymer solutions (Harper and Row; New York, 1970).
(5)Cassassa, E. F.Thermodynamic interactions in dilute polymer solutions, p. 151. IUPAC Macromolecular Microsymposia VIII and IX (London; Butterworth, 1972).
(6)Wilkinson, E. M. and Gordon, M.Determinants of Petrie matrices, Pacific J. Math. (in the Press).
(7)Edwards, S. F. Private communication.
(8)Edwards, S. F.A note on the divergence of the perturbation method in field theory. Philos. Mag. ser. 7, 45 (1954), 758.
(9)Gordon, M., Ross-Murphy, S. B. and Suzuki, H. Combinatorialapproach tothe excluded volume perturbation, submitted to Macromolecules.
(10)Brooks, R. L., Stone, A. H., Smith, C. A. B. and Tutte, W. T.The dissection of rectangles into squares. Duke Math. J. 7 (1940), 312340.
(11)Trent, H. M.A note on the enumeration and listing of all possible trees in a connected linear graph. Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 10041007.
(12)Tutte, W. T.A class of Abelian groups. Canad. J. Math. 8 (1956), 1328.
(13)Tutte, W. T.The number of planted plane trees with a given partition. Amer. Math. Monthly 71 (1964), 272277.

On sums of determinants of intersection matrices of Petrie matricest

  • M. Gordon (a1) and W. T. Tutte (a1)

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