Title: Super Rogers-Szegö polynomials associated with $BC_N$ type of Polychronakos spin chains,
Abstract: As is well known, multivariate Rogers-Szegö 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-Szegö (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.