An ordered class (A, <) is said to have cofinal (resp. coinitial) character a if a; is the least ordinal < On such that there is a cofinal (resp. coinitial) subclass of (A, <) that is isomorphic to a (resp. *a = the inverse of a). While having no impact on the proofs of the paper's other results, statement (iii) of Theorem 4 of [1, p. 1237] contains a minor error: it fails to mention that "(A, ...

Ž n . For a Hamming space X , d , the set of n-length words over the alphabet a H 4 n X s 0, 1, . . . , a y 1 endowed with the distance d , which for two words x s a H Ž . n Ž . n x , . . . , x , y s y , . . . , y g X counts the number of different components, 1 n 1 n a we determine the maximal cardinality of subsets with a prescribed diameter d or, in another language, anticodes with distance ...

Abstract Let $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, explicit description the summands involved in decomposition theorem applied to such has been obtained paper second author. Starting from this result, we provide Poincaré polynomial intersection c...

The class of Borel sets in a locally compact space is the cr-ring generated by the compact sets [3, p. 219], while the class of weakly Borel sets is the (r-algebra generated by the closed sets [2]. The object of this note is to show that any measure defined on the class of Borel sets may be extended to the class of weakly Borel sets in a simple and canonical way (Theorem 1). There is a useful a...

Erdos and Rado defined a A-system, as a family in which every two members have the same intersection. Here we obtain a new upper bound on the maximum cardinality q ( n , q ) of an n-uniform family not containing any A-system of cardinality q. Namely, we prove that, for any a > 1 and q , there exists C = C(a, q ) such that, for any n ,

Using the u-plane integral of Moore and Witten, we derive a simple expression for the Donaldson invariants of product ruled surfaces Σg × S, where Σg is a Riemann surface of genus g. This expression generalizes a theorem of Morgan and Szabó for g = 1 to any genus g. We give two applications of our results: (1) We derive Thaddeus’ formulae for the intersection pairings on the moduli space of ran...

Generalizing results of L. Fejes Tóth [3], [5], we prove the following theorem. Let R be a convex domain of area |R| and let S be a finite family of at least two congruent circles of total area t . Then for the area |F | of the part of R covered by the circles of S, the inequality |F | < t f (|R|/t) holds, where f (x) is the area of the intersection of a circle of unit area and a regular hexago...