U_{m,n} =

[I_{n} J_{n,m}]

[J_{m,n} 0_{m} ]

and

V_{m,n}=

[I_{n} J_{n,m}]

[J_{m,n} J_{m,m}]

We conjecture that V_{m,n} is cohesive but not barycentric for
1 < n < m + √m and that it is not cohesive for n ≥ m +
√m. We prove that it is cohesive for 1 < n < m + √m and
not cohesive for n ≥ 2m and confirm the conjecture computationally
for n < 2m ≤ 200. We also show that U_{m,n} is barycentric.

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