1324- and 2143-avoiding Kazhdan–Lusztig immanants and <i>k</i>-positivity

Abstract Immanants are functions on square matrices generalizing the determinant and permanent. Kazhdan–Lusztig immanants, which indexed by permutations, involve $q=1$ specializations of Type A polynomials, were defined Rhoades Skandera (2006, Journal Algebra 304, 793–811). Using results Haiman (1993, American Mathematical Society 6, 569–595) Stembridge (1991, Bulletin London 23, 422–428), showed that immanants nonnegative whose minors nonnegative. We investigate positive k -positive (matrices size $k \times k$ smaller positive). The immanant v is if avoids 1324 2143 for all noninversions $i&lt; j$ , either $j-i \leq or $v_j-v_i . Our main tool Lewis Carroll’s identity.