Equivariant Euler Characteristics on Permutohedral Varieties

Binomial coefficients can be interpreted as a solution to an intersection problem on a permutohedral variety \(X_E\) . Applying Hirzebruch-Riemann-Roch, this intersection problem is equivalent to computing Euler characteristic of a specific element of K-theory of \(X_E\) . This element has a natural lifting to equivariant K-theory and thus the Euler characteristic may be upgraded to a Laurent polynomial. We provide and implement three different approaches, in particular a recursive one, to computing these polynomials.