1992
DOI: 10.1090/s0002-9947-1992-1062874-3
|View full text |Cite
|
Sign up to set email alerts
|

Growth series of some wreath products

Abstract: Abstract.The growth series of certain finitely generated groups which are wreath products are investigated. These growth series are intimately related to the traveling salesman problem on certain graphs. A large class of these growth series is shown to consist of irrational algebraic functions.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
41
0

Year Published

1995
1995
2024
2024

Publication Types

Select...
6
2

Relationship

0
8

Authors

Journals

citations
Cited by 47 publications
(41 citation statements)
references
References 2 publications
0
41
0
Order By: Relevance
“…Then by Proposition 4.2 we may assume the group has a DCS-biautomatic structure with normal form the set of all Shortlex geodesics. Parry [37] proved that the bounded geodesic length problem for Z 2 ≀ Z 2 is NP-complete. So if such an algorithm could be constructed to run in polynomial time, we would have P=NP.…”
Section: It Follows That Dcs-biautomatic Does Not Imply Solvable Conjmentioning
confidence: 99%
“…Then by Proposition 4.2 we may assume the group has a DCS-biautomatic structure with normal form the set of all Shortlex geodesics. Parry [37] proved that the bounded geodesic length problem for Z 2 ≀ Z 2 is NP-complete. So if such an algorithm could be constructed to run in polynomial time, we would have P=NP.…”
Section: It Follows That Dcs-biautomatic Does Not Imply Solvable Conjmentioning
confidence: 99%
“…In the plane, finding a minimal length path between a specified set of points is equivalent to the travelling salesman problem. Thus, though the word problem for Z 2 ≀ (Z × Z) is straightforward, the question of determining minimal-length representatives is NP-hard, as shown by Parry [16].…”
Section: It Follows Immediately That |W| = D(w)mentioning
confidence: 99%
“…We shall also exhibit a natural, infinitely generated subgroup G 0 such that Nf G (G 0 ) has all the above properties and is of convergent type, so that Theorem 2 applies. These examples are based on Parry [32].…”
Section: Example 1 (Free Groups) Letmentioning
confidence: 99%
“…Parry [32] shows how this can be done when the Cayley graph of H is a (necessarily homogeneous) tree T . Here, we explain this in the (not really restrictive) case when…”
Section: Its Unit Element Is (Idmentioning
confidence: 99%
See 1 more Smart Citation