Steiner systems and configurations of points
نویسندگان
چکیده
منابع مشابه
Configurations in Steiner triple systems
" Combinatorial Designs and their Applications " c 1999 (copyright owner as specified in the book).
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The main result of this paper is the determination of all pairwise nonisomorphic trade sets of volume at most 10 which can appear in Steiner triple systems. We also enumerate partial Steiner triple systems having at most 10 blocks as well as configurations with no points of degree 1 and tradeable configurations having at most 12 blocks.
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Let F be a (0, 1) matrix. A (0, 1) matrix M is said to have F as a configuration if there is a submatrix of M which is a row and column permutation of F . We say that a matrix M is simple if it has no repeated columns. For a given v ∈ N, we shall denote by forb(v,F) the maximum number of columns in a simple (0, 1) matrix with v rows for which F does not occur as a configuration. We say that a m...
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Subsets of a v-set are in one-to-one correspondence with vertices of a v-dimensional unit cube, a Delaunay polytope of the lattice Z v. All vertices of the same cardinality k generate a (v?1)-dimensional root lattice A v?1 and are vertices of the Delaunay polytope P(v; k) of the lattice A v?1. Hence k-blocks of a t ? (v; k;) design, being identiied with vertices of P(v; k), generate a sub-latti...
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A defuzzification function assigns to each fuzzy set a crisp value in a way that this value may intuitively be understood as the “centre” of the fuzzy set. In the present paper, this vague concept is put into a mathematically rigorous form. To this end, we proceed analogously to the case of sharply bordered subsets, for which the Steiner point is frequently used. The function assigning to each ...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2020
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-020-00815-x