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On sums of determinants of intersection matrices of Petrie matricest

Published online by Cambridge University Press:  24 October 2008

M. Gordon
Affiliation:
University of Essex and University of Waterloo, Ontario
W. T. Tutte
Affiliation:
University of Essex and University of Waterloo, Ontario

Extract

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.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

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