Showing papers in "Journal of Combinatorial Theory, Series A in 1973"

TL;DR: An infinite sequence of finite or denumerable limit sets is found for a class of many-to-one transformations of the unit interval into itself and the structure and order of occurrence is universal for the class.

TL;DR: A simple theorem on generating functions is proved which can be used to establish the asymptotic normality of an(k) as a function of k and local limit theorems are turned to in order to obtain asymPTotic formulas for an( k).

TL;DR: A drawing strategy is explained which applies to a wide class of combinatorial and positional games and when applied to n -dimensional Tic-Tac-Toe, it improves a result of Hales and Jewett.

TL;DR: A construction is given for difference sets in certain non-cyclic groups with the parameters v, k, λ, n, which has minus one as a multiplier for every prime power q and every positive integer s.

TL;DR: Questions of whether or not certain R are r -Ramsey where B is a Euclidean space and R is defined geometrically are investigated.

TL;DR: Knowing estimates of the maximal length of simple circuits in certain 3-connected planar graphs are surveyed and improved in several directions.

TL;DR: The existence problem for t-designs with prescribed parameters is solved by allowing positive and negative integral multiplicities for the blocks.

TL;DR: The object of this paper is to report that the number of codewords of weight 15 is zero, thus reducing the number-of-unknown weights to two.

TL;DR: A proof is given of the result that, if real n-dimensional Euclidean space Rn is covered by any n + 1 sets, then at least one of these sets is such that each distance d(0) is integers.

TL;DR: A method of reduction is developed which, given a complementing system of m sequences, leads under certain conditions to a derived complementingSystem of m − 1 sequences.

TL;DR: In this paper, it is shown that for the graph if λ = 1, then the graph exists for all υ such that ν ≢ 2 mod 3.

TL;DR: The different combinatorial types of triangulations of the 3-sphere with up to 8 vertices are determined and it is shown that one cannot always preassign the shape of a facet of a 4-polytope.

TL;DR: A complete classification is given for neighborly 4-polytopes with 9 vertices and it is found that there are exactly 23 combinatorial types.

TL;DR: It is given a counterexample to a conjecture of L. D. Baumert about zeros of copositive matrices and those matrices in E which are on extreme rays of the cone ofCopositiveMatrices which are positive semidefinite, respectively.

TL;DR: New results in the theory of non-serial dynamic programming are described and their computational relevance is pointed out.

TL;DR: For any prime p, the sequence of Catalan numbers a n = 1 n 2n−2 n−1 is divided by the an prime to p into blocks Bk(k > 0) of an divisible by p, whose lengths and positions are determined.

TL;DR: One consequence of this generating function is a formula which can be regarded as a q-analog of a well-known result arising in the representation theory of the symmetric group.

TL;DR: This paper determines the minimum number of quadruples such that each pair of elements of S is contained in at least one of them for all n divisible by 3.

TL;DR: A new proof is given of the following theorem of Turyn: Let q = 2 n − 1 be a prime power ≡1 (mod 4); then there exists an Hadamard matrix of order 4 n that is of the Williamson type.

TL;DR: There are at most three sets of extendable symmetric design parameters with any given value of λ, and the only twice-extendable asymmetric design is the 21-point projective plane.

TL;DR: A common strengthening of the theorem that if A1, …, Al are subsets of a set S with n elements such that Ai ∩ Aj ≠ ∅ for all i, j then l ⩽ (k−1n−1) is proved.

TL;DR: The problem is solved for |M| ⩽ 2, and some partial results are obtained in the general case.

TL;DR: Let q be a number all whose prime factors divide integers of the form 2s − 1, s odd, if n = q + 2, the (3n) triples on n marks can be partitioned into q sets, each forming a Steiner triple system.

TL;DR: A family T of k-subsets of an n-set such that no more than r have pairwise fewer than s elements in common is maximum (for sufficiently large n) only if T consists of all the k-sets containing at least one of r fixed disjoint s- Subsets.

TL;DR: In case the structure is a generalized polygon, the irreducible representations of the algebra are computed and the theorem of Feit-Higman is deduced.

TL;DR: Hall's theorem on distinct representatives is proved that there exists an infinite sequence on X with discrepancy at most 1 and this result is very close to the best possible.

TL;DR: It is shown that the pairs (2-element subsets; edges of the complete graph) of a set of cardinality ℵ 1 can be colored with 4 colors so that every uncountable subset contains pairs of every color.