  As is well known, multivariate Rogers-Szeg\"o polynomials are closely
connected with the partition functions of the $A_{N-1}$ type of Polychronakos
spin chains having long-range interactions. Applying the `freezing trick', here
we derive the partition functions for a class of $BC_N$ type of Polychronakos
spin chains containing supersymmetric analogues of polarized spin reversal
operators and subsequently use those partition functions to obtain novel
multivariate super Rogers-Szeg\"o (SRS) polynomials depending on four types of
variables. We construct the generating functions for such SRS polynomials and
show that these polynomials can be written as some bilinear combinations of the
$A_{N-1}$ type of SRS polynomials. We also use the above mentioned generating
functions to derive a set of recursion relations for the partition functions of
the $BC_N$ type of Polychronakos spin chains involving different numbers of
lattice sites and internal degrees of freedom.
