论文标题
1324-和2143避免使用Kazhdan-Lusztig Immanants和K-Potitivity
1324- and 2143-avoiding Kazhdan-Lusztig immanants and k-positivity
论文作者
论文摘要
内在的功能是概括决定因素和永久性的正方形矩阵。由排列索引的Kazhdan-Lusztig Immanants涉及$ Q = 1 $ a型A型kazhdan-lusztig多项式的专业，并在（Rhoades-Skandera，2006年）中定义。使用（Haiman，1993年）和（Stembridge，1991）的结果，Rhoades和Skandera表明，Kazhdan-Lusztig Immanants对未成年人不负的矩阵不负。我们调查哪些Kazhdan-Lusztig Immanants对$ K $阳性矩阵（矩阵的矩阵，其尺寸$ k \ times k $ shoumer的矩阵均为正）。我们表明，当$ v $ $ k $ v $ $ v $避免1324和2143时，由$ v $ ty $ v $索引的kazhdan-lusztig内在索引为正，并且对于所有非反转$ i <j $ of $ v $，$ j-i \ j-i \ leq k $或$ v_j j $ v_j-jj-v_ji \ leq k $。我们的主要工具是刘易斯·卡罗尔（Lewis Carroll）的身份。
Immanants are functions on square matrices generalizing the determinant and permanent. Kazhdan-Lusztig immanants, which are indexed by permutations, involve $q=1$ specializations of Type A Kazhdan-Lusztig polynomials, and were defined in (Rhoades-Skandera, 2006). Using results of (Haiman, 1993) and (Stembridge, 1991), Rhoades and Skandera showed that Kazhdan-Lusztig immanants are nonnegative on matrices whose minors are nonnegative. We investigate which Kazhdan-Lusztig immanants are positive on $k$-positive matrices (matrices whose minors of size $k \times k$ and smaller are positive). We show that the Kazhdan-Lusztig immanant indexed by $v$ is positive on $k$-positive matrices when $v$ avoids 1324 and 2143 and for all non-inversions $i<j$ of $v$, either $j-i \leq k$ or $v_j-v_i\leq k$. Our main tool is Lewis Carroll's identity.
