Showing papers in "Journal of Combinatorial Theory, Series A in 1978"

TL;DR: Asymptotics are obtained for the number of n × n symmetric non-negative integer matrices subject to the following constraints: each row sum is specified and bounded, and a specified “sparse” set of entries must be zero.

TL;DR: If the simplicial complex formed by the neighborhoods of points of a graph is (k − 2)-connected then the graph is not k-colorable, and Kneser's conjecture is proved, asserting that if all n-subsets of a (2n − k)-element set are divided into k + 1 classes, one of the classes contains two disjoint n- subsets.

TL;DR: The characters of the adjacency algebra of Ω, which yield the MacWilliams transform on q-distance enumerators, are expressed in terms of generalized Krawtchouk polynomials.

TL;DR: C over GF(4) which have even weights and have the same weight distribution as the dual code C⊥ are studied, and an upper bound obtained on the minimum distance is obtained.

TL;DR: In the proof, it is shown two n - k degree homogeneous polynomials in n variables are equal by applying induction to those terms lacking one variable.

TL;DR: A short proof is given for Kneser's conjecture based on Borsuk's theorem and on a theorem of Gale.

TL;DR: It is proved that the minimum cardinality of a subset of AG which intersects all hyperplanes is k ( q − 1) + 1, and in case k = 2 this settles a conjecture of J. Doyen.

TL;DR: Whenever F is an extremal family the authors can find a 7-3 Steiner system B such that F consists exactly of those k -subsets of X which contain some member of B .

TL;DR: This paper proves that the minimal network for Σ is the tree of shortest total length LM(Σ) whose vertices are exactly the points of S, but the proof is sufficiently complicated that immediate generalization to arbitrary n, no matter how desirable, is unlikely.

TL;DR: A combinatorial proof of the Mehler formula on Hermite polynomials is given that is based upon the techniques of the partitional complex.

TL;DR: A short proof is given of the following conjecture of Minc: a n × n − (0, 1)-matrix with ri ones in row i = 1 n r i !

TL;DR: It is proved that the dimension of a semiorder is at most 3, to characterize semiorders of dimension 3 and height 2, and to prove Hiraguchi's Theorem.

TL;DR: This note contains a list of (v, k, λ) difference sets in noncyclic groups, for k using LaSalle's inequality.

TL;DR: The concept of a {Σα=1k wα, m; t, s}-min · hyper with weight is introduced and using this concept and the structure of a finite projective geometry PG(n − 1, s), a geometrical method of constructing a maximal Lt(t + r, s)-set is given.

TL;DR: Recurrence rules are derived for enumerating the linked diagrams first encountered by Touchard in 1952 and a recurrence rule is given for the number of symmetric irreducible diagrams, which enables one to calculate thenumber of symmetry-reduced irredUCible diagrams.

TL;DR: This elliptic semiplane cannot be realized as a projective plane minus a Baer subset, and is the first elliptIC semiplane constructed which has this property.

TL;DR: A family of sets {A k } is called a strong d system if the intersection of any two of its members is the same, i .e .

TL;DR: The purpose of this paper is to correct this defect and extend the result to Steiner quadruple systems (SQS) through methods of universal algebra as well as combinatorial methods.

TL;DR: A combinatorial proof of the main result would be very desirable since this could lead the way to more general result, q -analogs, and perhaps even a q-analog of MacMahon's Master Theorem.

TL;DR: It is shown in Theorem 1 that the authors can always choose i = 2 or 3, and that max ti = max(t2, t 3).

TL;DR: It is proved that any set of 2 k −2 + 1 points in R 2 contains a set of k points which form a convex polygon.

TL;DR: A theory of generating functions in countably many non-commuting variables is presented, which generalizes the theory of context free languages and applications are given to compositions of a number, rooted planar tree, dissected polygons, and the Theory of simple random walks.

TL;DR: Useful lower bounds are obtained for mt(r, s), s a prime power, r ⩾ t ⩽ 3, by relating (t − 1)-flats of PG(r − 1, s) to ( t − 1) and lower dimensional flats of its subgeometries.

TL;DR: The companion result for the secant numbers is proved and the number of alternating permutations with specified peak set is calculated.

TL;DR: An exhaustive computer search has established the existence of precisely four biplanes with k = 9 and one of the self-dual biplanes is new and a description is provided in terms of its automorphism group.