Showing papers in "Journal of Combinatorial Theory, Series A in 1999"

TL;DR: The main result states that ?(Gn) is shellable, in particular, Cohen?Macaulay, which can be further translated to say that the Stanley?Reisner ring of ?

TL;DR: A class of numbers, called Catalan-like numbers, are introduced which unify many well-known counting coefficients, such as the Catalan numbers, the MotzkinNumbers, the middle binomial coefficients, the hexagonal numbers, and many more.

TL;DR: The transition semigroup of the additive coalescent is shown to involve probability distributions associated with a multinomial expansion over rooted forests.

TL;DR: Given a setU of sizeq in an affine plane of orderq, the possibilities for the number of directions of secants of U are determined, and in many cases the setsU with given number of secant directions are characterized.

TL;DR: In this paper, an explicit expression for the generating series for the number of ramified coverings of the sphere by the double torus, with elementary branch points and prescribed ramification type over infinity, was obtained.

TL;DR: It is shown that, except for a few cases with small d, these difference sets are all pairwise inequivalent, and further applications of the 2-rank formulas are given, including the determination of the nonzeros of certain binary cyclic codes, and a criterion in terms of the trace function.

TL;DR: It is proved thatlimn?∞t3(n, 4)(n3)?3+1712=0.593592?

TL;DR: Novelli et al. as mentioned in this paper presented a bijective proof of the hook-content formula for tableaux of a given shape that does not involve the involution principle of Garsia and Milne.

TL;DR: Proving a conjecture of Wilf and Stanley in hitherto the most general case that for any layered pattern there is a constant so that it is avoided by less thancnpermutations of lengthn will imply the solution of this conjecture for at least 2 patterns of lengthk.

TL;DR: An explicit expression for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity, was given in this paper.

TL;DR: A number of results are obtained about the distribution ofN(R) including its asymptotic expectation and a bound on the probability that N(R)=0, and it is proved most Latin squares of ordernhaveN( R)?n3/2?

TL;DR: It is proved that for any c1>0 there exists c2>0 such that the following state- ment is true: If G is a graph with n vertices and with the property that neither G nor its complement contains a complete graph Kl, where l=c1logn then G is c2logn-universal, i.e., G contains all subgraphs with c2 logn vertices as induced sub graphs.

TL;DR: It is shown that if two partitions ?

TL;DR: Three classes of finite structures are related by extremal properties: complete d-partite d-uniform hypergraphs, d-dimensional affine cubes of integers, and families of 2d sets forming a d- dimensional Boolean algebra, and extremal results for each are reviewed and new ones for Boolean algebras andhypergraphs are derived.

TL;DR: The new semifield flock ofPG is constructed associated with the Penttila?Williams translation ovoid and the associated generalized quadrangle and its translation dual are studied.

TL;DR: This work proves explicit formulas for the number of lozenge tilings of these hexagons containing the central unit rhombus and obtains Propp's conjecture as a corollary of these results.

TL;DR: An elegant combinatorial rule for the generation of Schubert polynomials based on box diagrams is proved, which was conjectured by A. Kohnert, and the well-known fact that the Schuber polynOMials associated to Grassmannian permutations are in fact Schur polynmials is derived from Kohner's rule.

TL;DR: The present paper gives two direct proofs of the identity, which is equivalent to a refinement of Bott's formula for the affine Coxeter groupCn, and is the first truly bijective proof ever found in the domain of lecture hall partitions.

TL;DR: A Bruck?Ryser type condition is derived and some results on graphs with three eigenvalues, not all integral; these are a natural generalization of the strongly regular conference graphs.

TL;DR: During the course of the proof, some techniques for computing sub-Pfaffians of a given skew-symmetric matrix are developed and an open problem is presented which generalizes the Littlewood formula.

TL;DR: The aim of this note is to show how existing product constructions for cyclic and 1-rotational block designs can be adapted to provide a highly effective method of obtaining product theorems for whist tournaments.

TL;DR: Several results on perrank of a matrix are proved, motivated in part by the Alon?Jaeger?Tarsi Conjecture, which defines the perrank to be the size of the largest square submatrix of the matrix with nonzero permanent.

TL;DR: The Weil conjectures are applied to the Hessenberg varieties to obtain information about the combinatorics of descents in the symmetric group and elementary linear algebra leads to elegant proofs of some identities from the theory ofdescents.

TL;DR: This construction gives an infinite series of cyclically resolvable cyclic Steiner 2-designs with block size 4 on 4ppoints, wherep=12t+1 is a prime greater than 22581507 andtis odd.

TL;DR: Ordinary analytical techniques would be extremely unwieldy, and so a method is developed for attacking this problem by considering a related problem on tiling the integers by considered a set of powers of that operator and derive fixed-point results.

TL;DR: This article determines the setJR(v) forv?3(mod6) (only 10 cases are left undecided forv=15, 21, 27, 33, 39) and establishes that JR(v)=I(v), which is the set of all integersksuch that there exists a pair ofKTS( v) with preciselyktriples in common.

TL;DR: If every member of F is measurable or if every member is a Baire set, then one members of F must contain a sequence with all of its finite sums and products (and, in the measurable case,all of its infinite sums as well).

TL;DR: These inequalities are dual to each other for planar graphs and the second is tight up to a factor of 2 for trees; this has implications for a herd of gnus crossing a river delta.

TL;DR: The particular case a = b = c solves a problem posed by Propp and the result can be viewed as the enumeration of plane partitions having a rows and b columns, with largest entry ⩽ c.

TL;DR: This paper introduces a measure of the extent to which a finite combinatorial structure is a Ramsey object in the class of objects with a similar structure and shows how this measure depends on the symmetries of the structure.