Immanant preserving and immanant converting maps
نویسندگان
چکیده
منابع مشابه
Hecke Algebra Characters and Immanant Conjectures
The main purpose of this article is to announce and provide supporting evidence for two conjectures about the characters of the Hecke algebra Hn(q) of type An_I' evaluated at elements of its Kazhdan-Lusztig basis. In addition, we prove a conjectured immanant inequality for Jacobi-Trudi matrices (definitions below) and show how our conjectures would imply stronger inequalities of a similar kind....
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In 1992, Goulden and Jackson found a beautiful determinantal expression for the immanant of a matrix. This paper proves the same result combinatorially. We also present a β-extension of the theorem and a simple determinantal expression for the irreducible characters of the symmetric group.
متن کاملOn Goulden-jackson’s Determinantal Expression for the Immanant
In 1992, Goulden and Jackson found a beautiful determinantal expression for the immanant of a matrix. This paper proves the same result combinatori-ally.
متن کاملDeterminant versus Permanent: salvation via generalization? The algebraic complexity of the Fermionant and the Immanant
The fermionant Fermn(x̄) = ∑ σ∈Sn (−k)c(π) ∏n i=1 xi,j can be seen as a generalization of both the permanent (for k = −1) and the determinant (for k = 1). We demonstrate that it is VNP-complete for any rational k , 1. Furthermore it is #P -complete for the same values of k. The immanant is also a generalization of the permanent (for a Young diagram with a single line) and of the determinant (whe...
متن کاملEla the K-th Derivatives of the Immanant and the Χ-symmetric Power of an Operator∗
In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2006
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.01.030