Showing papers in "Journal of Combinatorial Theory, Series A in 1975"

TL;DR: The number of nonisomorphic designs on v points with given block size k > 2 and index λ tends to infinity as v increases (subject to the above congruences).

TL;DR: A complete classification is given of all [22, 11] and [24, 12] binary self-dual codes, giving the order of its group, the number of codes equivalent to it, and its weight distribution.

TL;DR: Improved asymptotic lower bounds to the Ramsey function R(k, t), with symmetric case k = t and more general case t = t is given.

TL;DR: Use Hindman's theorem as a strong pigeonhole principle to prove strengthened versions of Ramsey's theorem and of various generalizations of Ramsey’s theorem due to Nash-Williams, Galvin and Prikry, and Silver.

TL;DR: In this paper, the Williamson type and Goethals-Seidel matrices were combined by introducing F-matrices, which are a generalization of both Williamson and GSE matrices, for the new orders 119, 171, 185, 217 and the new classes 1 4 q(q + 1), q ≡ 3(mod 8) a prime power and 1 2 p(p − 3), p ≡ 1(mod 4) and p − 4 both prime powers.

TL;DR: This paper improves upon previously known upper bounds for kα,β(m, n) by proving that k αβ (m,n)⩾ 1+((β−1) ( p α−1 ))( m α ) + ((p+1)(α− 1) α )n for each integer p greater than or equal to α − 1.

TL;DR: It is shown that a necessary condition for the existence of a maximal arc (as a proper subset of a given plane 7r(q) is that n should be a factor of q, and it is proved that this condition does suffice in the case of any desarguesian plane of order 2 h.

TL;DR: An algorithm for determining a nonlinear de Bruijn sequence of length 2 n requiring only 3 n bits of storage is described and a collection of crossjoins are found which can be applied to the sequence to produce a large class of related de bruijn cycles.

TL;DR: It is proved that the amount of uncovered area can always be kept down to at most proportional to α 7 11, which for large α is much less than the linear waste produced by the “natural” packing above.

TL;DR: It is shown that such a hexagon is unique and has an area exceeding that of a regular hexagon of unit diameter by about 4%.

TL;DR: Three extension theorems for t-designs are proved; two for t even, and one for t odd, and another theorem guaranteeing that certain t- designs be (t + 1)-designs is presented.

TL;DR: This paper presents a direct recursive proof of the fact that the binary increasing trees are equinumerous with half of the alternating permutations considered by Andre, and exhibits a natural bijection between the two families.

TL;DR: In [3], the following result was proved: any abelian permutation group is quasiregular, and if F denotes the fixed sub- structure of[', then one of the following must hold.

TL;DR: It is shown that for any n, there exist subsets of an n × n square array containing n points, of which no three lie in a line, and that for sufficiently large n there exist such subsets containing (32 − ϵ)n points.

TL;DR: It is shown that among BIB designs with parameters, the incidence matrix of the BIB design PG(t, 2):t − 1 derived from a finite projective geometry PG( t, 2) has the minimum 2-rank.

TL;DR: Robert Donaghey's discovery of the first result was the occasion for this paper, which presents all results in a single setting, and shows the enumerator by endpoints including the root to be f n (x).

TL;DR: It is proved that D(2v + 1) > v + 1 + D( v) for v > 3 where D(v) denotes the maximum number of pairwise disjoint Steiner triple systems of order v.

TL;DR: A is partition regular in G if for every partition of G/(0) into finitely many classes there exist elemens x1,…,xm contained in one class such that A(x1,…., xm)T = 0.

TL;DR: This paper explores some restricted Ramsey theorems, best illustrated by the following beautiful result of NeSetIil and RodI.

TL;DR: A natural bijection between (v, 3, 2)-BIBD's and certain topological and combinatorial structures related to graph imbeddings is used to obtain new classes of designs of this type.

TL;DR: In the study of the biochemistry of the DNA molecule, one is led to postulate models of behavior in which the molecule is treated like a “word,” and the individual bases arranged on the molecule are the “letters.”

TL;DR: A large class of one-to-one correspondences is given between acyclic and parking functions, generalizing a previous construction given by Foata and Riordan.

TL;DR: A general principle for selecting at random from a collection of combinatorial objects, where " at random " means in such a way that each of the objects has equal probability, a priori, of being selected.

TL;DR: A generalization of Hall's Multiplier Theorem for difference sets is given and some nonexistence theorems are also given to compile a table of addition sets with parameter k≤10.

TL;DR: The purpose of this paper is to add yet another class of Hadamard matrices to the ever growing list of constructions, and to prove the following results.

TL;DR: By what amounts to determining a few terms in a continued fraction expansion of A(z), it is able to obtain sufficiently accurate rational approximations to A(Z) to show that 01 = 0.14185325f 6 x 1O-8 and that 1.794147176 < h <1.794 147186.

TL;DR: A generalized quadrangles of order 3 must be isomorphic either to the quadrangle P 4 or to its dual, where P 4 consists of all points of PG(3, 3) and those lines of PG self-conjugate with respect to a null polarity.