منابع مشابه
Immanants of Totally Positive Matrices Are Nonnegative
If/ is an irreducible character of Sn, these functions are known as immanants; if/ is an irreducible character of some subgroup G of Sn (extended trivially to all of Sn by defining /(vv) = 0 for w$G), these are known as generalized matrix functions. Note that the determinant and permanent are obtained by choosing / to be the sign character and trivial character of Sn, respectively. We should po...
متن کاملKazhdan-Lusztig immanants III: Transition matrices between canonical bases of immanants
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 کاملthe second immanant of some combinatorial matrices
let $a = (a_{i,j})_{1 leq i,j leq n}$ be an $n times n$ matrixwhere $n geq 2$. let $dt(a)$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$. let $g$ be a connected graph with blocks $b_1, b_2, ldots b_p$ and with$q$-exponential distance matrix $ed_g$. we given an explicitformula for $dt(ed_g)$ which shows that $dt(ed_g)$ is independent of the manner in ...
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Let S be a subset of diagonal entries of an n × n complex matrix A. When the members of S have a common value which is equal to an eigenvalue of A, then S is a critical diagonal set of A. The existence of such a set is equivalent to the matrix Ã, obtained from A by setting its diagonal entries equal to zero, having an s × t zero submatrix with s + t ≥ n + 1. If S is a minimal critical diagonal ...
متن کاملSome Remarkable Combinatorial Matrices
In this paper we describe, in combinatorial terms, some matrices which arise as Laplacians connected to the three-dimensional Heisenberg Lie algebra. We pose the problem of finding the eigenvalues and eigenvectors of these matrices. We state a number of conjectures including the conjecture that all eigenvalues of these matrices are non-negative integers. We determine the eigenvalues and eigenve...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1992
ISSN: 0021-8693
DOI: 10.1016/0021-8693(92)90196-s