Showing papers in "Journal of Combinatorial Theory, Series A in 2001"

TL;DR: Two combinatorial problems for the set Fnq of sequences of length n over the alphabet Fq={0, 1, ?, q?1} are considered and simple algorithms to recover X?Fnq from N?q(n, t)+1 of its subsequences oflength n?t and from N+q( n, t) of its supersequences of Length n+t are given.

TL;DR: It is shown that the minimum possible cardinality of such a set F is precisely 1+?mi=1(ki?1) for every sequence of integers k1, k2, ?, km?2

TL;DR: It is shown that the determinants det0?i, j?n?1(??ij+(m+i+jj)), where ? is any 6th root of unity, are variations of a famous result due to Andrews (1979, Invent. Math.53, 193?225).

TL;DR: The following theorem concerning the poset of all subsets of n] ordered by inclusion is proved: there exist |S| disjoint saturated chains containing all the subsets in S and R.

TL;DR: This work extends the result of Furstenberg and Glasner on piecewise syndeticity to apply to infinitely many notions of largeness in arbitrary semigroups and to partition regular structures other than arithmetic progressions.

TL;DR: It is shown that for any ?

TL;DR: It is proved that Z4p is a CI-group; i.e., two Cayley graphs over the elementary abelian group Z4P are isomorphic if and only if their connecting sets are conjugate by an automorphism of the group Z 4p.

TL;DR: It is shown that small blocking sets in PG(n, q) with respect to hyperplanes intersect every hyperplane in 1 modulo p points, where q=ph, which can be used to characterize certain non-degenerate blocking set in higher dimensions.

TL;DR: It is shown that the optimal upper bound obtainable from Delsarte's linear program will strictly exceed the Gilbert?Varshamov lower bound and the McEliece, Rodemich, Rumsey, and Welch upper bound.

TL;DR: Using the Garcia?Stichtenoth curves, infinite classes of (n, m, w)-perfect hash families with |H|=O(logn) for fixed m and w are obtained, which are among the most efficient explicit constructions for perfect hash families known in the literature.

TL;DR: In this paper, it is shown that the product of an m-chain with an n-chain, m and n both >1, is sign-balanced if and only if m?n mod2.

TL;DR: It is shown that for every c>0 there exists c?>0 satisfying the following condition.

TL;DR: Central and local limit theorems are derived for the number of distinct summands in integer partitions, with or without repetitions, under a general scheme essentially due to Meinardus.

TL;DR: It is shown that the maximum size of a B2-sequence of binary n-vectors for large enough n is at most 20.5753n, thus improving on the previous bound 20.6n due to B. Lindstrom.

TL;DR: A new decomposition of derangements is given, which gives a direct interpretation of a formula for their generating function, and this decomposition also works for counting derangement by number of excedances.

TL;DR: It is proved that only two examples exist for the locally quadrangular case, arising in Q(6, 2) and H(5, 4), respectively, and that, in this case, the geometry ?

TL;DR: A nonsymmetric Bush-type Hadamard matrix of order 36 is constructed which leads to two new infinite classes of symmetric designs with parameters, where m is any positive integer.

TL;DR: A characterization of (3+1)-free posets in terms of their antiadjacency matrices is given and it is shown that this characterization leads to a simple proof that the chain polynomial of a (3-1)- free poset has only real zeros.

TL;DR: The final result is to classify maximal arcs in Desarguesian projective planes whose collineation stabilisers are transitive on the points of the maximal arcs.

TL;DR: It is shown that the MacMahon symmetric functions are the generating functions for the orbits of sets of functions indexed by partitions under the diagonal action of a Young subgroup of a symmetric group.

TL;DR: It is proved that the size of such set systems satisfying Frankl?Wilson-type conditions modulo prime powers is polynomially bounded, in contrast with V. Grolmusz's recent result that for non-prime-power moduli, no polynomial bound exists.

TL;DR: The basic theory of ternary complementary pairs is redeveloped, showing how to construct all known pairs from a handful of initial pairs the authors call primitive, and all primitive pairs up to length 14 are displayed, more than doubling the number that could be inferred from the existing literature.

TL;DR: The Extended Riemann Hypothesis and recent results on the asymptotic existence of Hadamard matrices imply that for n sufficiently large r(n)>(12??)n, there is an r×n (1, ?1)-matrix H satisfying the matrix equation HH?=nIr.

TL;DR: The number of rhombus tilings of a hexagon with side lengths a, b, c, a,b, c which contain the central Rhombus is computed and the “almost central”rhombus above the centre is calculated.

TL;DR: This paper disproves the conjecture that the number of vectors of minimum weight in a sequence of binary linear codes of distance dn grows exponentially with the length.

TL;DR: It is proved that n(1)=3, n(2)=11, and n(3) is incomprehensibly large, and a lower bound is given for n( 3) in terms of the familiar Ackermann hierarchy.

TL;DR: A short proof of Z. Furedi's theorem (1990, J. Combin. Theory Ser. A55, 316?320) stated in the title is presented.

TL;DR: It is proved that the number of nonisomorphic Steiner triple systems on 2 n?1 points of 2-rank 2n?n grows exponentially.

TL;DR: Let s(G ) be the samllest integer t such that every sequence of t elements in G contains a zero-sum subsequence of length exp(G ), which has been studied by serveral authors during last 20 years.

TL;DR: The general form of the dual egg for eggs arising from a semifield flock is calculated and obtained using the egg obtained by L. Bader et al. from the Penttila?Williams ovoid, which is not isomorphic to any of the previous known examples.