The inhomogeneous $t$-PushTASEP and Macdonald polynomials

Arvind Ayyer, James Martin, Lauren Williams

We study a multispecies $t$-PushTASEP system on a finite ring of $n$ sites with site-dependent rates $x_1,\dots ,x_n$. Let $\lambda =({\lambda }_1,\dots ,{\lambda }_n)$ be a partition whose parts represent t…