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Phase Transitions in Infinitely Generated Groups, and Related Problems in Additive Number Theory
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Melvyn B. Nathanson
Veröffentlicht/Copyright:
4. August 2011
Abstract
Let A be an infinite set of generators for a group G, and let LA(r) denote the number of elements of G whose word length with respect to A is exactly r. The growth function LA is a function from the nonnegative integers ℕ0 to the set ℕ0 ∪ {∞}. The purpose of this note is to determine all growth functions associated to infinite generating sets for groups.
Received: 2009-09-30
Accepted: 2009-12-27
Published Online: 2011-08-04
Published in Print: 2011-August
© de Gruyter 2011
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Artikel in diesem Heft
- The Number of Solutions of λ(x) = n
- Monochromatic Sums Equal to Products in ℕ
- On the Sum of Reciprocal Generalized Fibonacci Numbers
- Recursively Self-Conjugate Partitions
- Modular Hyperbolas and the Coefficients of (x–1 + 6 + x)k
- Algebraic Proof for the Geometric Structure of Sumsets
- An Erdős–Fuchs Type Theorem for Finite Groups
- Coincidences of Catalan and q-Catalan Numbers
- Phase Transitions in Infinitely Generated Groups, and Related Problems in Additive Number Theory
- Perfect Numbers with Identical Digits
- Remarks on the Pólya–Vinogradov Inequality
- Heights of Divisors of xn – 1
- Bernoulli Numbers and Generalized Factorial Sums
- Witten Volume Formulas for Semi-Simple Lie Algebras
Schlagwörter für diesen Artikel
Additive Bases;
Infinitely Generated Groups;
Growth in Groups;
Geometric Group Theory
Artikel in diesem Heft
- The Number of Solutions of λ(x) = n
- Monochromatic Sums Equal to Products in ℕ
- On the Sum of Reciprocal Generalized Fibonacci Numbers
- Recursively Self-Conjugate Partitions
- Modular Hyperbolas and the Coefficients of (x–1 + 6 + x)k
- Algebraic Proof for the Geometric Structure of Sumsets
- An Erdős–Fuchs Type Theorem for Finite Groups
- Coincidences of Catalan and q-Catalan Numbers
- Phase Transitions in Infinitely Generated Groups, and Related Problems in Additive Number Theory
- Perfect Numbers with Identical Digits
- Remarks on the Pólya–Vinogradov Inequality
- Heights of Divisors of xn – 1
- Bernoulli Numbers and Generalized Factorial Sums
- Witten Volume Formulas for Semi-Simple Lie Algebras
