1324- and 2143-avoiding Kazhdan–Lusztig immanants and <i>k</i>-positivity
نویسندگان
چکیده
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 $i< j$ , either $j-i \leq or $v_j-v_i . Our main tool Lewis Carroll’s identity.
منابع مشابه
On permutations which are 1324 and 2143 avoiding
We consider permutations which are 1324 and 2143 avoiding, where 2143 avoiding means that it is 2143 avoiding with the additional Bruhat restriction {2 ↔ 3}. In particular, for every permutation π we will construct a linear map Lπ and a labeled graph Gπ and will show that the following three conditions are equivalent: π is 1324 and 2143 avoiding; Lπ is onto; Gπ is a forest. We will also give so...
متن کاملCounting 1324-Avoiding Permutations
We consider permutations that avoid the pattern 1324. By studying the generating tree for such permutations, we obtain a recurrence formula for their number. A computer program provides data for the number of 1324-avoiding permutations of length up to 20.
متن کاملoutputs Permutations avoiding 1324 and patterns in
The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets. By considering certain large subsets of the class, which consist of permutations with a particularly regular structure, we prove that the growth rate of the class exceeds 9.81. This improves on a previous lowe...
متن کاملCounting 1324, 4231-Avoiding Permutations
Classes of permutations are sets of permutations that are closed downwards under taking subpermutations. They are usually presented as sets C that avoid a given set B of permutations (i.e. the permutations of C have no subpermutation in the set B). We express this by the notation C = Av(B). Much of the inspiration for elucidating the structure of pattern classes has been driven by the enumerati...
متن کاملoutputs The enumeration of permutations avoiding 2143 and 4231
We enumerate the pattern class Av(2143, 4231) and completely describe its permutations. The main tools are simple permutations and monotone grid classes.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2021
ISSN: ['1496-4279', '0008-414X']
DOI: https://doi.org/10.4153/s0008414x21000262