For positive integers k ≥ 2, we consider the integrality of quotients of Wronskians involving certain normalizations of the Andrews-Gordon q-series ∏ 1≤n 6≡0,±i(mod2k+1) 1 1− qn . This study is motivated by the appearance of these series in conformal field theory as irreducible characters of Virasoro minimal modules. We establish an upper bound on primes p for which such quotients of Wronskians...

The G-values of various games, by R. K. Guy and C. A. B. Smith, introduced a broad class of impartial games and gave complete normalplay solutions for many of them. In this paper, we announce misère-play solutions to many of the games considered by Guy and Smith. They are described in terms of misère quotients—commutative monoids that encode the additive structure of specific misère-play games....

In earlier work we gave a characterisation of pregeometries which are ‘basic’ (that is, admit no ‘non-degenerate’ quotients) relative to two different kinds of quotient operation, namely taking imprimitive quotients and normal quotients. Each basic geometry was shown to involve a faithful group action, which is primitive or quasiprimitive, respectively, on the set of elements of each type. For ...

The G-values of various games, by R. K. Guy and C. A. B. Smith, introduced a broad class of impartial games and gave complete normalplay solutions for many of them. In this paper, we announce misère-play solutions to many of the games considered by Guy and Smith. They are described in terms of misère quotients—commutative monoids that encode the additive structure of specific misère-play games....

We extend previous computations of Calabi-Yau metrics on projective hypersurfaces to free quotients, complete intersections, and free quotients of complete intersections. In particular, we construct these metrics on generic quintics, four-generation quotients of the quintic, Schoen CalabiYau complete intersections and the quotient of a Schoen manifold with Z3 × Z3 fundamental group that was pre...

Ah, la recherche! Du temps perdu. Soit G le quotient du groupe libre a 26 g en era-teurs a; b; c; : : : ; z par les relations A = B, pour tout couple de mots (A; B) pouvant avoir la m^ eme prononciation en anglais. (Un groupe d eeni d'une mani ere analogue a et e consid er e dans Landsburg 1986].) Notre but est de d eterminer la structure du groupe G. Théorème. G est trivial. Démonstration. (No...

Given an action of an affine algebraic group with only trivial characters on a factorial variety, we ask for categorical quotients. We characterize existence in the category of algebraic varieties. Moreover, allowing constructible sets as quotients, we obtain a more general existence result, which, for example, settles the case of a finitely generated algebra of invariants. As an application, w...

If I is a monomial ideal with linear quotients, then it has componentwise quotients. However, the converse of this statement an open question. In paper, we provide two classes ideals for which holds. First class polymatroidal in K[x, y] and second one strong exchange property.

The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formal-language terms as the number of distinct quotients of the language, and to call it “quotient complexity”. The problem of ...