A nice involution for multivariable polynomial rings

Abstract

The principal minors of the Toeplitz matrix ${\left(x_{i-j+1}\right)}_{1\le i,j,\le n}$, where $x_0=1,x_k=0$ if $k\le -1$, directly determine an involution of the polynomial ring $R[x_1,...,x_n]$ over any commutative ring $R$.