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As is well known, multivariate Rogers-Szeg\"o polynomials are closelyconnected with the partition functions of the $A_{N-1}$ type of Polychronakosspin chains having long-range interactions. Applying the `freezing trick', herewe derive the partition functions for a class of $BC_N$ type of Polychronakosspin chains containing supersymmetric analogues of polarized spin reversaloperators and subsequently use those partition functions to obtain novelmultivariate super Rogers-Szeg\"o (SRS) polynomials depending on four types ofvariables. We construct the generating functions for such SRS polynomials andshow 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 generatingfunctions to derive a set of recursion relations for the partition functions ofthe $BC_N$ type of Polychronakos spin chains involving different numbers oflattice sites and internal degrees of freedom.

Super Rogers-Szeg\"o polynomials associated with $BC_N$ type of Polychronakos spin chains