Combinatorics on bi-${\hat{I}}^3$-positivity of $1/k$-Eulerian polynomials

Sherry H. F. Yan, Xubo Yang, Zhicong Lin

The $1/k$-Eulerian polynomials $A_n^{(k)}(x)$ were introduced as ascent polynomials over $k$-inversion sequences by Savage and Viswanathan. The bi-${\hat{I}}^3$-positivity of the $1/k$-Eu…