The $\mathrm{v}$-number of powers of ideals associated with chessboard complexes

We study the $\mathrm{v}$-numbers of ordinary and symbolic powers of the facet ideal and the Stanley–Reisner ideal of a chessboard complex. Exact formulas are established for the $\mathrm{v}$-numbers of ordinary and symbolic powers of the Stanley–Reisner ideal, as well as symbolic powers of the facet ideal. Furthermore, we show that the $\mathrm{v}$-number function of the ordinary powers is asymptotically linear.