# Algebraic, Extremal and Metric Combinatorics 1986 by M. M. Deza, P. Frankl, I. G. Rosenberg

By M. M. Deza, P. Frankl, I. G. Rosenberg

Because of papers from Algebraic, Extremal and Metric Combinatorics 1986 convention held on the college of Montreal, this e-book represents a entire evaluation of the current country of development in 3 comparable parts of combinatorics. subject matters coated within the articles comprise organization shemes, extremal difficulties, combinatorial geometries and matroids, and designs. the entire papers include new effects and lots of are wide surveys of specific parts of study.

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Japan, 31 (1979), 199-207. 7. E. Bannai and R. M. Damerell, Tight spherical designs, II, J. London Math. Soc. 21 (1980), 13-30. 8. E. Bannai and S. G. Hoggar, On tight t-designs in compact symmetric spaces of rank one, Proc. Japan Acad. 61A (1985), 78-82. 9. E. Bannai and S. G. Hoggar, Tight t-design in projective spaces and Newton polygons, Ars Combinatoria 20A (1985)' 43-49. 10. E. Bannai and S. G. Hoggar, Tight t-designs and squarefree integers, (preprint, submitted to Europ. J. ). 11. E •. Bannai and T.

And 7. Determine tight t-designs in These·three values of Remark: t Sd for t • 4, 5 are the only open cases. d d > 2 if there is a tight t-design in S , Note then we have a that if necessary condition which comes from a Pell equation, obtained by the R2 (x) (for t • 4), c 2 (x) (for t • 5), t • 7) are all rational numbers. ) Perhaps it should be possible also to treat the case X either antipodal or non-antipodal, assuming necessary). d + 4 t • 4)? 2. t • 2s - 1. t • 4. As is well known, if t t > 2s- 2, of Q-polynomial association scheme of class Remark: t • 2s - 2 (with is not too small if then X has a structure s, so they are expected to exist very rarely.

Then there is a natural vector space over K (of an appropriate dimension) on which naturally. G acts Also, there exists a natural (hermitian) inner product, and the points in Pd(K) are represented by vectors of the unit norm (with respect to the inner product). 2) For a finite subset X of M, we define (as before), A(X) = (l(x,y)l 2 1