Showing papers in "Journal of Combinatorial Theory, Series A in 1986"

TL;DR: On etablit quelques theoremes d'intersections pour les ensembles ordonnes and les graphes en utilisant la fonction d'entropie.

TL;DR: It is shown that m q (n,k,t), the maximum possible number of subspaces in a t-intersecting family F of k-dimensional subspaced of V, holds for all F, F′ ϵ F .

TL;DR: Two classes of n-edged maps on S as N → ∞: tree-rooted and tree- rooted smooth are asymptotically enumerated, based on a system of equations enumerating single vertex maps and on a relation found by Walsh and Lehman for the case of orientable surfaces between tree-ROoted and single vertices.

TL;DR: A new symmetry operation, called complementation, is introduced on plane partitions whose three-dimensional diagram is contained in a given box, based on the theory of Schur functions, in particular the Littlewood-Richardson rule.

TL;DR: A combinatorial interpretation of a formula of Frobenius relating the Stirling numbers of the second kind to the Eulerian polynomials leads to a number of results and conjectures concerning certain poynomials which may be viewed as q -analogues of the classical rook numbers.

TL;DR: The structure of minimal unsatisfiable CNF formulas in n variables containing precisely n + 1 clauses is characterised, and this characterization is given a geometric interpretation.

TL;DR: Here it is shown that gk,n = k·n for k n 2 .

TL;DR: It is proved that A and B are systems of k and l element subsets of an n element set respectively and that n −1 k −1 n − 1 l −1 , whenever n ⩽ 2k + l − 2 (k ⩾ l).

TL;DR: The Schensted correspondence is closely related to the decomposition of V ⊗ n as a GL(V) -module and is obtained in this paper.

TL;DR: This paper describes evidence which indicates a close connection between m by m alternating sign matrices and descending plane partitions with no parts exceeding m and gives several conjectures and a few theorems concerning self-complementary totally symmetric plane partitions.

TL;DR: A new, short proof of the Erdos-Ko-Rado theorem is given, which states that if F is a family of k-subsets of an n-set no two of which are disjoint, n ⩾ 2k, then |F| ⩽ n−1 k−1 holds.

TL;DR: A family of extremely simple bijections are constructed that yield Cayley's famous formula for counting trees and allow the calculation of explicit formulas for the expected number of various statistics on Cayley trees.

TL;DR: The proof of this formula is given by constructing bijection between permutations, trees, and words, which gives also a combinatorial proof of a formula appearing in the enumerative theory of planar maps.

TL;DR: This design is the smallest possible nontrivial simple 6-design that can exist and has full automorphism group cyclic of order 13.

TL;DR: It is proved by use of the classification of the doubly even (32, 16) codes, that in addition to the design formed by the planes in PG(4, 2), there are exactly four other nonisomorphic quasi-symmetric 2-(31, 7, 7) designs, and they all have 2-rank 16.

TL;DR: The theory of hooks, cores, and quotients of partitions of partitions is generalized to symbols, which index the characters of the so-called symbols.

TL;DR: The construction of Steiner quadruple systems of all orders n≡2 or 4 (mod 6) by Hanani and some recursive techniques are used to show that C(3, 4, n) = L(2, 3, 4) for all n ⩾ 52423.

TL;DR: The necessity of Eckhoffs inequalities is proved and the sufficiency of the Eckhoff inequalities are proved.

TL;DR: It is shown that the diagonal Ramsey number R 2 ( k + 1) > p and the size of the largest clique contained in G is k, which is well known.

TL;DR: It is proved that if υ ≡ 0 or 4 (mod 6), υ > 12, then there exists a twofold triple system of order υ having exactly k repeated triples if and only if k ϵ I′υ.

TL;DR: For any q ∈ {0, 1, …, r}, it is found necessary and sufficient conditions for G to have a detachment F without loops or multiple edges such that F(E1), …, F(Er) are almost regular and F( e1, E1, e1) are 2-edge-connected and each vertex ξ of G arises by identification from a prescribed number g(ξ) of vertices of F.

TL;DR: For spaces with infinitely many nonempty derivatives a strong negative theorem is obtained and it is possible to partition the pairs of rationals into countably many pieces so that every homeomorph of the rationals contains a pair from every piece.

TL;DR: The equivalence of three previously given definitions of the generalized Sprague-Grundy function G is established, and an optimal strategy for the sum of a wide class of two-player games which may contain cycles or loops is formulated, which is one of the main applications of G.

TL;DR: It is proved that v = pn for some prime p ≡ 3 (mod 4), n is odd and 1.

TL;DR: Asymptotic bounds are given on the maximal sum ∑ i =1 k t ( F i ) which can be realized by k different faces in an arrangement of n lines.

TL;DR: Generalisation du theoreme de Schur relatif aux partitions d'ensembles sous the forme d'un theoreME ergodique de densite sous la forme oficiale de densites.

TL;DR: Two new simple proofs that D(n), D (n, k) are finite are given, and D( n, 2) precisely for all n ⩾ 2 is determined.

TL;DR: A new approach which facilitates the calculation of the covering radius of a binary linear code based on determining the normalized covering radius ϱ is introduced, which leads to an amusing generalization of the Berlekamp-Gale switching game.

TL;DR: It is shown that the greatest element of a sum-distinct set of positive integers must exceed 2 −n ( n 2n )— asymptotically 4 π 1 2 times better than the hitherto best known bound.

TL;DR: It is shown that the problem of covering an n × n chessboard with a minimum number of queens on a major diagonal is related to the number-theoretic function r3(n), the smallest number of integers in a subset of {1,…,n} which must contain three terms in arithmetic progression.