Deformation cones of Tesler polytopes

For a ∈ $\begin{array}{} \displaystyle \mathbb{R}_{\geq 0}^{n} \end{array}$ , the Tesler polytope Tes n ( a ) is the set of upper triangular matrices with non-negative entries whose hook sum vector is a . We first give a different proof of the known fact that for every fixed a 0 ∈ $\begin{array}{} \displaystyle \mathbb{R}_{ \gt 0}^{n} \end{array}$ , all the Tesler polytopes Tes n ( a ) are deformations of Tes n ( a 0). We then calculate the deformation cone of Tes n ( a 0). In the process, we also show that any deformation of Tes n ( a 0) is a translation of a Tesler polytope. Lastly, we consider a larger family of polytopes called flow polytopes which contains the family of Tesler polytopes and chracterize the flow polytopes which are deformations of Tes n ( a 0).