Vertical perimeter versus horizontal perimeter

Assaf Naor, Robert Young

The discrete Heisenberg group ${\mathbb{H}}_{\mathbb{Z}}^{2k+1}$ is the group generated by $a_1,b_1,\dots ,a_k,b_k,c$, subject to the relations $[a_1,b_1]=\dots =[a_k,b_k]=c$ and $[a…