Finite differences and determinant identities

Partial Fractions and q-Binomial Determinant Identities

Partial fraction decomposition method is applied to evaluate a general determinant of shifted factorial fractions, which contains several Gaussian binomial determinant identities .

Genetic Differences and Human Identities

T his report is one product of a large project un-dertaken by The Hastings Center and the Amer-ican Association for the Advancement of Science and funded by the Ethical, Legal, and Social Implications division of the National Human Genome Research Institute. Mark Frankel and Audrey Chap-man (from AAAS) and I worked from the very beginning to develop the project and submit the grant application ...

Finite Models of Identities

Disjunctive Identities of Finite Groups and Identities of Regular Representations

The problem of describing identities of concrete algebraic structures is traditionally one of the most attractive in variety theory. Very often it is a difficult problem, and many deep works are entirely devoted to finding bases of identities of classical algebraic objects. This paper was initiated by attempts to find bases of identities for certain representations of finite groups. Let F be th...

Finite Rogers-Ramanujan Type Identities

Polynomial generalizations of all 130 of the identities in Slater’s list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new. The author has implemented much of the finitization process in a Maple package which is available for free do...