Hostname: page-component-7479d7b7d-qs9v7 Total loading time: 0 Render date: 2024-07-12T21:21:10.733Z Has data issue: false hasContentIssue false
  • English
  • Français

On sums of determinants of intersection matrices of Petrie matricest†‡

Published online by Cambridge University Press:  24 October 2008

M. Gordon  and
W. T. Tutte
M. Gordon
Affiliation:
University of Essex and University of Waterloo, Ontario
W. T. Tutte
Affiliation:
University of Essex and University of Waterloo, Ontario
Get access Rights & Permissions [Opens in a new window]

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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 2 , March 1974 , pp. 155 - 163
Copyright
Copyright © Cambridge Philosophical Society 1974

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Kendall, D. G.A statistical approach to Flinders Petrie–s sequence dating. Bull. Inst. Internat. Statist. 40 (1963), 657–680.Google Scholar
(2)Kendall, D. G.A mathematical approach to seriation. Philos. Trans. Roy. Soc. Lond. Scr. A269 (1970), 125–134.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), 312–340.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), 1004–1007.Google Scholar
(12)Tutte, W. T.A class of Abelian groups. Canad. J. Math. 8 (1956), 13–28.CrossRefGoogle Scholar
(13)Tutte, W. T.The number of planted plane trees with a given partition. Amer. Math. Monthly 71 (1964), 272–277.CrossRefGoogle Scholar