Lower bounds for some Ramsey numbers

AbstractLet n, r, u1, u2,…,uk be positive integers satisfying ui ⩾ r for i = 1,2,…,k. The symbol n → (u1, u2,…,uk)r means that, for any partition of the r-subsets of an n-set S into k classes C1, C2,…,Ck, there is a ui-subset of S all of whose r-subsets belong to Ci for some i, 1 ⩽ i ⩽ k. A theorem of F.P. Ramsey asserts that, if r, u1, u2,…,uk are given, then n → (u1, u2,…,uk)r for all sufficiently large n. n ↦ (u1, u2,…,uk)r denotes the negation of n → (u1, u2,…,uk)r. In this paper a number of results of the form n ↦ (u1, u2,…,uk)3 are obtained

Further results on snakes in powers of complete graphs

AbstractBy a snake in a finite graph G is meant a cycle without chords. Denoted by S(G) the length of a longest snake in G. In this paper we obtain a new lower bound for S(G) in the case where G is the product of d copies of the complete graph on n vertices

On property B(s), II

AbstractDenote by m(n,s) the size of a smallest family F; of n-element sets with the property that if |S∩F|⩾1 for all F∈F, then |S∩F|⩾s for some F∈F;. We obtain some bounds for m(n,s)

On the snake in the box problem

AbstractA snake in a graph is a simple cycle without chords. Denote by s(d) the length of a longest snake in the d-dimensional unit cube. We give a new proof of the theorem of Evdokimov that s(d) > λ2d, where λ is a positive constant

Ramsey numbers for triples

AbstractSome recurrence inequalities for Ramsey numbers for triples are established by means of explicit constructions

Asymptotically hyperbolic manifolds with small mass

For asymptotically hyperbolic manifolds of dimension $n$ with scalar curvature at least equal to $-n(n-1)$ the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to hyperbolic space. In this paper we study asymptotically hyperbolic manifolds which are also conformally hyperbolic outside a ball of fixed radius, and for which the positive mass theorem holds. For such manifolds we show that the conformal factor tends to one as the mass tends to zero

Prospects for Searching for Excited Leptons during RunII of the Fermilab Tevatron

This letter presents a study of prospects of searching for excited leptons during RunII of the Fermilab Tevatron. We concentrate on single and pair production of excited electrons in the photonic decay channel in one CDF/DO detector equivalent for 2 fb^{-1}. By the end of RunIIa, the limits should be easily extended beyond those set by LEP and HERA for excited leptons with mass above about 190 GeV.Comment: 4 pages, 8 figure

Electroweak Radiative Corrections to Neutral-Current Drell-Yan Processes at Hadron Colliders

We calculate the complete electroweak O(alpha) corrections to pp, pbar p -> l+l- X (l=e, mu) in the Standard Model of electroweak interactions. They comprise weak and photonic virtual one-loop corrections as well as real photon radiation to the parton-level processes q bar q -> gamma,Z -> l+l-. We study in detail the effect of the radiative corrections on the l+l- invariant mass distribution, the cross section in the Z boson resonance region, and on the forward-backward asymmetry, A_FB, at the Fermilab Tevatron and the CERN Large Hadron Collider. The weak corrections are found to increase the Z boson cross section by about 1%, but have little effect on the forward-backward asymmetry in the Z peak region. Threshold effects of the W box diagrams lead to pronounced effects in A_FB at m(l+l-) approx 160 GeV which, however, will be difficult to observe experimentally. At high di-lepton invariant masses, the non-factorizable weak corrections are found to become large.Comment: Revtex3 file, 39 pages, 2 tables, 12 figure

Energy Flow in Interjet Radiation

We study the distribution of transverse energy, Q_Omega, radiated into an arbitrary interjet angular region, Omega, in high-p_T two-jet events. Using an approximation that emphasizes radiation directly from the partons that undergo the hard scattering, we find a distribution that can be extrapolated smoothly to Q_Omega=Lambda_QCD, where it vanishes. This method, which we apply numerically in a valence quark approximation, provides a class of predictions on transverse energy radiated between jets, as a function of jet energy and rapidity, and of the choice of the region Omega in which the energy is measured. We discuss the relation of our approximation to the radiation from unobserved partons of intermediate energy, whose importance was identified by Dasgupta and Salam.Comment: 26 pages, 8 eps figures. Revised to include a discussion of non-global logarithm