1324- and 2143-avoiding Kazhdan-Lusztig immanants and k-positivity
نویسندگان
چکیده
منابع مشابه
Kazhdan-lusztig Immanants and Products of Matrix Minors, Ii
We show that for each permutation w containing no decreasing subsequence of length k, the Kazhdan-Lusztig immanant Immw(x) vanishes on all matrices having k equal rows or columns. Also, we define two filtrations of the vector space of immanants via products of matrix minors and pattern avoidance and use the above result to show that these filtrations are equivalent. Finally, we construct new an...
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We define a family of polynomials of the form ∑ f(σ)x1,σ(1) · · ·xn,σ(n) in terms of the Kazhdan-Lusztig basis {C′ w(1) |w ∈ Sn} for the symmetric group algebra C[Sn]. Using this family, we obtain nonnegativity properties of polynomials of the form ∑ cI,I′∆I,I′(x)∆I,I′(x). In particular, we show that the application of certain of these polynomials to Jacobi-Trudi matrices yields symmetric funct...
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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...
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We study two bases of the vector space of immanants of C[x1,1, . . . , xn,n]: the bitableaux basis of Désarménien-Kung-Rota, and a subset of the dual canonical basis called the basis of Kazhdan-Lusztig immanants. We show that the transition matrix between these bases is unitriangular, describe new vanishing results for the Kazhdan-Lusztig immanants, and relate both bases to other immanants defi...
متن کاملKazhdan-Lusztig Polynomials for 321-Hexagon-Avoiding Permutations
In (Deodhar, Geom. Dedicata, 36(1) (1990), 95–119), Deodhar proposes a combinatorial framework for determining the Kazhdan-Lusztig polynomials Px,w in the case where W is any Coxeter group. We explicitly describe the combinatorics in the case where W = Sn (the symmetric group on n letters) and the permutation w is 321-hexagon-avoiding. Our formula can be expressed in terms of a simple statistic...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2021
ISSN: 0008-414X,1496-4279
DOI: 10.4153/s0008414x21000262