56 citations · 120 across the 14 of their papers we have counts for
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math.GR2014★ 6 cited
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…
math.GR2014★ 2 cited
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…