A short proof for the polynomiality of the stretched littlewood-Richardson coefficients

<p> The stretched Littlewood-Richardson coefficient \(c^{t\nu}_{t\lambda,t\mu}\) was conjectured by King, Tollu, and Toumazet to be a polynomial function in \(t\). It was shown to be true by Derksen and Weyman using semi-invariants of quivers. Later, Rassart used Steinberg's formula, the hive conditions, and the Kostant partition function to show a stronger result that \(c^{\nu}_{\lambda,\mu}\) is indeed a polynomial in variables \(\nu, \lambda, \mu\) provided they lie in certain polyhedral cones. Motivated by Rassart's approach, we give a short alternative proof of the polynomiality of \(c^{t\nu}_{t\lambda,t\mu}\) using Steinberg's formula and a simple argument about the chamber complex of the Kostant partition function. </p>