Combinatorial differential geometry and ideal Bianchi–Ricci identities II – the torsion case

Combinatorial Differential Topology and Geometry

A variety of questions in combinatorics lead one to the task of analyzing the topology of a simplicial complex, or a more general cell complex. However, there are few general techniques to aid in this investigation. On the other hand, the subjects of differential topology and geometry are devoted to precisely this sort of problem, except that the topological spaces in question are smooth manifo...

Geometry II - Discrete Differential Geometry

Some Combinatorial and Analytical Identities

We give new proofs and explain the origin of several combinatorial identities of Fu and Lascoux, Dilcher, Prodinger, Uchimura, and Chen and Liu. We use the theory of basic hypergeometric functions, and generalize these identities. We also exploit the theory of polynomial expansions in the Wilson and Askey-Wilson bases to derive new identities which are not in the hierarchy of basic hypergeometr...

Binomial Identities - Combinatorial and Algorithmic

The problem of proving a particular binomial identity is taken as an opportunity to discuss various aspects of this eld and to discuss various proof techniques in an examplary way. In particular, the unifying r^ ole of the hypergeometric nature of binomial identities is underlined. This aspect is also basic for combinatorial models and techniques, developed during the last decade, and for the r...

Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves Ii: Tripods and Combinatorial Cuspidalization

Let Σ be a subset of the set of prime numbers which is either equal to the entire set of prime numbers or of cardinality one. In the present paper, we continue our study of the pro-Σ fundamental groups of hyperbolic curves and their associated configuration spaces over algebraically closed fields in which the primes of Σ are invertible. The starting point of the theory of the present paper is a...