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math.CO2026
On the Dimension of the Best-Worst Choice Polytope
Keivan Mallahi-Karai, Majid Salamat
For a set of alternatives, the best--worst choice polytope is the convex hull of the deterministic best--worst choice vectors induced by all linear rankings of the alternatives…
math.CO2026
An infinite family of trees with irreducible characteristic polynomials
Saieed Akbari, Keivan Mallahi-Karai
Consider the tree obtained by attaching a leaf to the third vertex of a path with n-1 vertices. In this note, we prove that the characteristic polynomial of this tree is irreducibl…
math.PR2026
Random free semigroups of affine groups
Richard Aoun, Keivan Mallahi-Karai
We investigate random freeness of semigroups in the solvable non-virtually nilpotent setting. We focus on a correlated affine model, namely semigroups generated by the two componen…