as In an 2k+l values The paper concludes with the N(d, k) an;-alSJI[)HJ~i and circuit cove1'ings then show that certain fi1.1'(Yl1lll1'.r We introduce shows This new result also our present the values d and n 5.100. INTRODUCTION A directed or 'Unl"llllll. G where (i) II is nonempty set 11 , •• 1 v n1 , •• } of distinct elements called vertices; (ii) E is called arcs. E = {el' e2, ... 1 em,"'} o...

The ju-invariant fi(M) of an oriented Z2 -homology 3-sphere M is defined by Hirzebruch in [8], using Rohlin's Theorem [13], to be the mod 16 reduction of the signature of a framed manifold W with M = dW. In this paper we give a formula for p(M) by studying M as a branched dihedral covering space of S 3 . Hilden [7] and Montesinos [9] have independently shown that every closed orientable 3-manif...

Using combinatorial methods, we prove the following theorem on the group S of all permutations of a countably-infmite set: Whenever p 6 S has infinite support without being a fixed-point-free involution, then any s G S is a product of three conjugates of p. Furthermore, we present uncountably many new conjugacy classes C of S satisfying that any s G S is a product of two elements of C. Similar ...

Using fibre bundle theory we construct the universal covering group of U(n), Ũ(n), and show that Ũ(n) is isomorphic to the semidirect product SU(n)©s R. We give a bijection between the set of projective representations of U(n) and the set of equivalence classes of certain unitary representations of SU(n) ©s R. Applying Bargmann’s theorem, we give explicit expressions for the liftings of project...

Abstract. Let G be a group of automorphisms of a category C. We give a definition for a functor F : C → C to be a G-covering and three constructions of the orbit category C/G, which generalizes the notion of a Galois covering of locally finitedimensional categories with group G whose action on C is free and locally bonded. Here C/G is defined for any category C and does not require that the act...

For prime power q, we determine the minimum number of parallel classes in a resolvable 2-(kq, L 1) covering for almost all values of k. @ 1999 Elsevier Science B.V. All rights reserved In September 1995 Jan van Haastrecht gave a dinner on the occasion of his retirement. He had invited 20 colleagues. The host and the guests were to be seated at three tables each of which had seven places. The di...

It is a well-known phenomenon in set theory that problems in infinite combinatorics involving singular cardinals and their successors tend to be harder than the parallel problems for regular cardinals. Examples include the behaviour of cardinal exponentiation, the extent of the tree property, the extent of stationary reflection, and the existence of non-free almost-free abelian groups. The expl...

More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or noninherited quadratic forms. It was subsequently known as the BPX multigrid framework, which was widely used in the analysis of multigrid and domain decomposition methods. However, the framework has an apparent limit in the analysis of nonnested V-cycle methods, and...