Infinite words and length functions.

Title: Infinite words and length functions.
Identifier: AAI3103168
identifier: 3103168
Creator: Serbin, Denis E.
Contributor: Adviser: Alexei Miasnikov
Date: 2003
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: Let F = F(X) be a free group with basis X and Z [t] be a ring of polynomials in variable t with integer coefficients. The main result of the first part of this thesis is the representation of elements of Lyndon's free Z [t]-group FZt by infinite words defined as sequences w : [1, fw] → X+/-1 over closed intervals [1, fw], fw ≥ 0, in the additive group Z [t]+, viewed as an ordered abelian group. This representation provides a natural regular free Lyndon length function w → fw on FZt with values in Z [t]+. The second part of the thesis is concerned with applications of the construction above to finitely generated subgroups of F Z [t]. Finitely generated subgroups of F Z [t] are associated with combinatorial objects called ( Z [t], X)-graphs study of which solves some algorithmic problems for these subgroups such as the membership problem, the conjugacy problem etc.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.