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Combinatorial homotopy of simplicial complexes and complex information systems. (English) Zbl 0886.05122
Cox, David A. (ed.) et al., Applications of computational algebraic geometry. American Mathematical Society short course, San Diego, CA, USA, January 6–7, 1997. Providence, RI: American Mathematical Society. Proc. Symp. Appl. Math. 53, 91-118 (1998).
The paper deals with combinatorial homotopy or “A-homotopy” for simplicial complexes. This concept is derived from “Q-analysis”, as introduced by R. Atkin. The paper contains all the relevant definitions for combinatorial fundamental groups or “A-homotopy groups”, as well as a brief introduction to Gröbner bases in free associative algebras. These Gröbner bases are then used for an algorithmic computation of the A-homotopy groups. The algebraic concepts are related to the analysis of complex information systems.
For the entire collection see [Zbl 0880.00039].

05E99 Algebraic combinatorics
16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
94A15 Information theory (general)