The work of Fulkerson and Gross on incidence matrices shows that the question, whether a given incidence matrix A can be so re-arranged by rows as to bring together all the Γs in each separate column, can be settled if one merely knows A through the symmetrised product A T A. Suppose it is known that such a row re-arrangement exists; it is proved here that A can then be re-arranged in the required way if one merely knows A through the dual symmetrised product, AA T . Thus A T A and AA T contain respectively (i) information sufficient to decide on the possibility or otherwise of such a re-arrangement, and (ii) information sufficient to determine a sorting algorithm. Implications for archaeology are briefly discussed.
[1]
David G. Kendall,et al.
Some problems and methods in statistical archaeology
,
1969
.
[2]
Automorphisms of groups of similitudes over $F_{3}$.
,
1969
.
[3]
Mary Shaw,et al.
Computer analysis of chronological seriation
,
1967
.
[4]
D. R. Fulkerson,et al.
Incidence matrices and interval graphs
,
1965
.
[5]
J. Kruskal.
Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
,
1964
.
[6]
W. S. Robinson.
A Method for Chronologically Ordering Archaeological Deposits
,
1951,
American Antiquity.