Hypergeometric Groups Research Articles

Hypergeometric and Generalized Hypergeometric Group Testing

We consider two group testing problems involving a set of n items. In the first problem extactlyd defectives, and in the second problem at mostd defectives, are distributed arbitrarily in the set. We show that any procedure for identifying all defectives in the first problem can be easily adapted to the second problem, with an increase of at most one in the maximum number of tests required. Some related problems are also described.

A Note on Hypergeometric Group Testing Procedures

We consider two group testing problems. In the first problem there are $n + 1$ items including exactly d defectives. In the second problem there are n items including at most d defectives. We show that for every nested group testing procedure solving one of the two problems in t tests assuming worst case, we can construct a nested procedure solving the other problem also in t tests.

O určení základních substitucí hypergeometrické grupy pomocí Wirtingerovy formule

O určení základních substitucí hypergeometrické grupy pomocí Wirtingerovy formule

Invariants of hypergeometric groups for Calabi-Yau complete intersections in weighted projective spaces

Let Y be a Calabi-Yau complete intersection in a weighted projective space. We show that the space of quadratic invariants of the hypergeometric group associated with the twisted I-function is one-dimensional, and spanned by the Gram matrix of a split-generator of the derived category of coherent sheaves on Y with respect to the Euler form.