75 citations · 85 across the 12 of their papers we have counts for
12 papers
Growth in higher Baumslag-Solitar groups
Ayla P. Sánchez, Michael Shapiro
We study the HNN extension of given by the cubing endomorphism , and prove that such groups have rational growth. To do so, we describe a method of com…
Rational growth in the Heisenberg group
Moon Duchin, Michael Shapiro
A group presentation is said to have rational growth if the generating series associated to its growth function represents a rational function. A long-standing open question asks w…
Equations in nilpotent groups
Moon Duchin, Hao Liang, Michael Shapiro
We show that there exists an algorithm to decide any single equation in the Heisenberg group in finite time. The method works for all two-step nilpotent groups with rank-one commut…
Groups that do and do not have context-sensitive word problem
Derek F. Holt, Sarah Rees, Michael Shapiro
We prove that a group has word problem that is a growing context-sensitive language precisely if its word problem can be solved using a non-deterministic Cannon's algorithm (the de…
On a generalization of Dehn's algorithm
Oliver Goodman, Michael Shapiro
Viewing Dehn's algorithm as a rewriting system, we generalise to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of g…
Regular geodesic normal forms in virtually abelian groups
Walter Neumann, Michael Shapiro
Cannon has given an example of a virtually abelian group and a generating set where the full language of geodesics is not regular. We describe a virtually abelian group and a gener…