Showing papers in "Journal of Combinatorial Theory, Series A in 1971"

TL;DR: In this article, a class of orthomodular lattices which admit no bounded measures was constructed, and the purpose of this paper is to construct a set of such lattices.

TL;DR: In this paper, the authors considered the problem of estimating the distance between two points in k-dimensional Euclidean space, where the minimum is assumed over all possible choices of X1,..., X,.

TL;DR: In this article, it was shown that every finite incomplete Steiner triple system (totally symmetric loop) can be embedded in a finite complete Steiner Steiner triangulation.

TL;DR: In this article, an order-preserving map from k-dimensional subspaces into k-element subsets has been proposed, where each subspace of an n-dimensional vector space ove GF(q) is assigned a number p and a partition of p into at most k parts not exceeding n − k, in such a way that exactly qp of the subspace map into a given partition.

TL;DR: A new design with parameters (79, 13, 2) is constructed and the question of possible collineation groups for a symmetric design with given parameters ( v, k, λ) is considered.

TL;DR: This paper provides methods (suitable for the computer) by which to construct orthogonal circulant matrices of any size, and finds the orders of these groups for n prime to p, and shows how to construct Gsp, Ssp, Osp from Gs, Ss, Os.

TL;DR: In this article, it was shown that for any three positive integers k, n and m, there exists a closed sequence (ordered cycle) of k m-ary digits 0, 1,…, m − 1 such that the k subsequences of n consecutive digits are all different.

TL;DR: A majority decoding method, quite similar to Massey's threshold decoding, is devised for the Golay code and various related codes.

TL;DR: In this article, the classical theory of Riemann surfaces was used to derive the following combinatorial theorem: if π 1,…, π m are permutations of 1, 2,…, n, such that π 2,π 1,π m = 1, then v(π 1 ) + π + v (π m ) ⩾ 2(n − t ), where t is the number of orbits of the cyclic group generated by the permutation π acting on the set {1,…, n }, and �

TL;DR: In this paper, it was shown that any finite topology with n points which is not discrete contains (7/16)2" open sets and in the opposite direction, topologies with a small number of open sets are TO-space.

TL;DR: The Bruck-Ryser theorem is stated that, if the order s = 1 or 2 (4) and if the decomposition of s contains a prime of the form 4k + 3 to an odd power, then the finite projective plane fails to exist.

TL;DR: It is proved that M ( 5, 4) ⩽ 28 and M (5, 5)⩽ 55 are integers and new upper bounds are given for M ( 6, 4), M (6, 5), and M(6, 6).

TL;DR: A rather general and extremely useful result, which gives a necessary condition that certain Veblen-Wedderburn systems coordinatize isomorphic translation planes, is contained in Section 7 of the paper.

TL;DR: The relationship between symmetry operators of Kranz products with abelian characters and their underlying subgroups is explored and some applications to combinatorics are discussed.

TL;DR: This paper generalizes the results of Sperner determining the maximal number of subsets of a given set, such that no one is included in the other, by modifying the restrictive condition.

TL;DR: In this paper, it was shown that Spernernerner's conjecture on non-comparable subsets of a set holds for arbitrary geometric lattices, namely, that the maximal number of noncomparable elements in a finite geometric lattice is max w(k), where w is the number of elements of rank k.

TL;DR: In this article, the Fourier transform of a periodic sequence from GF(q) = F is used to define the smallest integer ω for which it is possible to write 1 as a product of ω conjugates of roots of f.

TL;DR: The generalized quadrangles of order (s, t ) constructed by Ahrens and Szekeres and by Hall as discussed by the authors were shown to yield a rather more general construction, where s = q − 1, t = q + 1, q any prime power.

TL;DR: In this article, it was shown that a finite partial idempotent Latin square can be embedded in a finite idemic Latin square, which is then shown to be Hopfian.

TL;DR: In this article, the Fundamental Lemma of Complexity (strong form) was proved for all semigroups considered in this paper, and the results of [4, Chapters 1, 5-91] were announced in [5].

TL;DR: In this article, the existence, the structure, and the number of 2-manifolds such that M is a 2-complex contained in the 2-dimensional skeleton of P, and containing all the edges of P.

TL;DR: This paper shows how to construct a Latin square orthogonal to its transpose for every order n, such that n ≢ 2 mod 4, or n ≡= 3 mod 9 or n≢ 6 mod 9.

TL;DR: Results for (n − 1) -dimensional spaces over fields of n elements are obtained with the aid of combinatorial results arising from the study of hypercubes.

TL;DR: The block structure of this type of design is examined, and this information is used to construct eight new solutions for (16, 24, 9, 6, 3); along with the Bhattacharya design, these are the only known counterexamples for λ = 3.

TL;DR: Theorem 1.1.1 of as mentioned in this paper generalizes the theorem from the trivial character 1G to all generalized characters and shows that the class function which dominates counting is actually a generalized character of G.