Advanced determinant calculus: A complement

Advanced Determinant Calculus: a Complement

This is a complement to my previous article “Advanced Determinant Calculus” (Séminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory (G. Almkvist, J. Petersson and the author, Experiment. Math. 12 (2003), 441– ...

Advanced Determinant Calculus

The purpose of this article is threefold First it provides the reader with a few useful and e cient tools which should enable her him to evaluate nontrivial de terminants for the case such a determinant should appear in her his research Second it lists a number of such determinants that have been already evaluated together with explanations which tell in which contexts they have appeared Third ...

Fermion Determinant Calculus

The path-integral of the fermionic oscillator with a time-dependent frequency is analyzed. We give the exact relation between the boundary condition to define the domain in which the path-integral is performed and the transition amplitude that the path-integral calculates. According to this relation, the amplitude suppressed by a zero mode does not indicate any special dynamics, unlike the anal...

A Calculus for Graphs with Complement

We present a system for deriving inclusions between graphs from a set of inclusions between graphs taken as hypotheses. The novel features are the extended notion of graph with an explicitly representation of complement, the more involved definition of the system, and its completeness proof due to the embedding of complements. This is an improvement on former work, where complement was introduc...

Multivariable Advanced Calculus