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Merino-Welsh inequalities for matroids with controlled lattices of cyclic flats
Beke, Csáji, Csikvári, and Pituk showed that the Merino--Welsh quotient $Φ(M)=T_M(1,1)^2/(T_M(2,0)T_M(0,2))$ can be arbitrarily large, so the multiplicative Merino-Welsh inequality fails for matroids in general. We show that $Φ$ is uniformly bounded on the class of matroids whose cyclic-flat lattice
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