Results 1 to 10 of about 78 (66)

Immanant Conversion on Symmetric Matrices

Special Matrices, 2014
Letr Σn(C) denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C) -> Σn (C) satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB) = dχ·(
Alexander Guterman
exaly   +2 more sources

Immanant preserving and immanant converting maps

Linear Algebra and Its Applications, 2006
An immanant, associated to an irreducible complex character \(\chi\) of symmetric group \(S_n\), is a function \(d_\chi:M_n({\mathbb F})\to {\mathbb F}\), defined by \[ d_\chi(A):=\sum_{\sigma\in S_n}\chi(\sigma)\prod^n_{i=1}a_{i\sigma(i)} \qquad\forall A=(a_{ij})\in M_n({\mathbb F}).
Purificação Coelho, M., Antónia Duffner, M.   +1 more
exaly   +2 more sources

Path tableaux and combinatorial interpretations of immanants for class functions on $S_n$ [PDF]

Discrete Mathematics & Theoretical Computer Science, 2011
Let $χ ^λ$ be the irreducible $S_n$-character corresponding to the partition $λ$ of $n$, equivalently, the preimage of the Schur function $s_λ$ under the Frobenius characteristic map.
Sam Clearman, Brittany Shelton, Mark Skandera   +2 more
doaj   +1 more source

An immanant formulation of the dual canonical basis of the quantum polynomial ring [PDF]

Discrete Mathematics & Theoretical Computer Science, 2009
We show that dual canonical basis elements of the quantum polynomial ring in $n^2$ variables can be expressed as specializations of dual canonical basis elements of $0$-weight spaces of other quantum polynomial rings.
Mark Skandera, Justin Lambright
doaj   +1 more source

%-Immanants and Temperley-Lieb Immanants

, 2023
42 pages, 11 ...
Lu, Frank, Ren, Kevin, Shen, Dawei, Wang, Siki   +3 more
openaire   +2 more sources

The second immanant of some combinatorial matrices [PDF]

Transactions on Combinatorics, 2015
Let $A = (a_{i,j})_{1 leq i,j leq n}$ be an $n times n$ matrix where $n geq 2$. Let $dt(A)$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$.
R. B. Bapat, Sivaramakrishnan Sivasubramanian   +1 more
doaj  

Vanishing immanants

Linear Algebra and its Applications
21 pages, 3 ...
Cheraghpour, Hassan, Kuzma, Bojan
openaire   +3 more sources

The stabilizer of immanants

Linear Algebra and its Applications, 2011
We describe immanants as trivial modules of the symmetric group and show that any homogeneous polynomial of degree n on the space of n by n matrices preserved up to scalar by left and right action by diagonal matrices and conjugation by permutation matrices is a linear combination of immanants.
openaire   +3 more sources

The Second Immanantal Polynomial for the Signless Laplacian Matrix of a Graph

Axioms
The second immanantal polynomial is one of the important directions in algebraic theory. Let M=[mij] be an n×n matrix. The second immanant of matrix M is defined as d2(M)=∑σ∈Snχ(σ)∏i=1nmiσ(i), where χ is the irreducible character of the symmetric group ...
Yafan Geng, Tingzeng Wu
doaj   +1 more source

The (n-1)-th Laplacian Immanantal Polynomials of Graphs

Axioms
Let χn−1(σ) denote the irreducible character of the symmetric group Sn corresponding to the partition (n−1,1). For an n×n matrix M=(mi,j), we denote its (n−1)-th immanant by dn−1(M).
Wenwei Zhang, Tingzeng Wu, Xianyue Li
doaj   +1 more source