Lovász, Spencer and Vesztergombi proved that the linear discrepancy of a hypergraph H is bounded above by the hereditary discrepancy of H, and conjectured a sharper bound that involves the number of vertices in H. In this paper we give a short proof of this conjecture for hypergraphs of hereditary discrepancy 1. For hypergraphs of higher hereditary discrepancy we give some partial results and p...

H is the theory extending β-conversion by identifying all closed unsolvables. Hω is the closure of this theory under the ω-rule (and β-conversion). A long-standing conjecture of H. Barendregt states that the provable equations of Hω form a Π11-complete set. Here we prove that conjecture.

Let H be the corner-transfer-matrix Hamiltonian for the six-vertex model in the antiferroelectric regime. It acts on the infinite tensor product W = V ⊗ V ⊗ V ⊗ · · ·, where V is the 2-dimensional irreducible representation of the quantum affine Lie algebra Uq ( ŝl (2) ) . We observe that H is the derivation of Uq ( ŝl (2) ) , and conjecture that the eigenvectors of H form the level-1 vacuum re...

Let C ⊂ Pr be a general curve of genus g embedded via a general linear series of degree d. The well-known Maximal Rank Conjecture asserts that the restriction maps H(OPr(m)) → H(OC(m)) are of maximal rank; if known, this conjecture would determine the Hilbert function of C. In this paper, we prove an analogous statement for the hyperplane sections of general curves. More specifically, if H ⊂ Pr...

Associative products are defined using a scheme of Imrich & Izbicki [18]. These include the Cartesian, categorical, strong and lexicographic products, as well as others. We examine which product ⊗ and parameter p pairs are multiplicative, that is, p(G ⊗ H) ≥ p(G)p(H) for all graphs G and H or p(G⊗H) ≤ p(G)p(H) for all graphs G and H. The parameters are related to independence, domination and ir...

Let X be a smooth projective variety over C of dimension d. Let ∆ ⊂ X × X be the diagonal. There is a cohomology class cl(∆) ∈ H(X ×X). In this paper we use Betti cohomology with rational coefficients. There is the Künneth decomposition H(X ×X) ≃ ⊕2d i=0 H (X)⊗H (X). We write cl(∆) = ∑2d i=0 π hom i according to this decomposition. Here π hom i ∈ H (X)⊗ H (X). If the Hodge conjecture is true, t...

If G and H are two cubic graphs, then an H-coloring of G is a proper edge-coloring f with edges of H , such that for each vertex x of G, there is a vertex y of H with f(∂G(x)) = ∂H(y). If G admits an H-coloring, then we will write H ≺ G. The Petersen coloring conjecture of Jaeger states that for any bridgeless cubic graph G, one has: P ≺ G. The second author has recently introduced the Sylveste...

We present a collection of results on a conjecture of Jannsen about the p-adic realizations associated to Hecke characters over an imaginary quadratic field K of class number 1. The conjecture is easy to check for Galois groups purely of local type (§1). In §2 we define the p-adic realizations associated to Hecke characters over K. We prove the conjecture under a geometric regularity condition ...

In the 20th century, many great mathematicians were attracted by this conjecture. In 1900, D. Hilbert gave a famous speech in an international mathematical conference, in which he proposed 23 problems to mathematicians. The Goldbach conjecture is a part of his 8th problem and the other part is the Riemann hypothesis. G. H. Hardy said that the Goldbach conjecture is one of the most difficult pro...

A conjecture of Komlós states that for every graph H, there is a constant K such that if G is any n-vertex graph of minimum degree at least (1 (1/ cr(H)))n, where cr(H) denotes the critical chromatic number of H, then G contains an H-matching that covers all but at most K vertices of G. In this paper we prove that the conjecture holds for all sufficiently large values of n. © 2003 Wiley Periodi...