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2010

New parameters of subsets in polynomial schemes

Suda, Sho

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We define new parameters, a zero interval and a dual zero interval, of subsets in $P$- or $Q$-polynomial schemes.

A zero interval of a subset in a $P$-polynomial scheme is a successive interval index for which the inner distribution vanishes, and a dual zero interval of a subset in a $Q$-polynomial scheme is a successive interval index for which the dual inner distribution vanishes.
We derive the bounds of the lengths of a zero interval and a dual zero interval using the degree and dual degree respectively, and show that a subset in a $P$-polynomial scheme (resp.
a $Q$-polynomial scheme) having a large length of a zero interval (resp.

New parameters of subsets in polynomial schemes · Around

Built on

P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rep. 10 (Suppl.) (1973)
1973
Earlier work this paper cites.
P. Delsarte, J. M. Goethals, J. J. Seidel, Spherical codes and designs, Geom. Dedicata 6 (1977), 363–388
1977
Earlier work this paper cites.

Similar

E. Bannai, T. Ito, Algebraic Combinatorics I: Association Schemes, Benjamin/Cummings, Menlo Park, CA, 1984
1984
Cited alongside, same era.
P. Seymour, T. Zaslavsky, Averaging sets: A generalization of mean values and spherical designs, Advs. in Math. 52 (1984), 213–240
1984
Cited alongside, same era.

Then

A. E. Brouwer, C. D. Godsil, J. H. Koolen, W. J. Martin, Width and dual width of subsets in polynomial association schemes, J. Combin. Theory Ser. A 102 (2003), no. 2, 255–271
2003
Later among the works it cites.

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