Let d k denote the normalized hook immanant corresponding to the partition (k, 1 "-k) of n. P. Heyfron proved the family of immanantal inequalities det A=e71(A) ~<t~2(A)-<< .--.<<d.(A) =perA (1) for all positive semidefinite Hermitian matrices A. Motivated by a conjecture of R. Merris, it was shown
Hook Immanantal Inequalities for Hadamard's Function
โ Scribed by Onn Chan; Bee-San Ng
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 124 KB
- Volume
- 299
- Category
- Article
- ISSN
- 0024-3795
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โฆ Synopsis
For an n ร n positive semi-definite (psd) matrix A, Peter Heyfron showed in [9] that the normalized hook immanants, dk , k = 1, . . . , n, satisfy the dominance ordering
๐ SIMILAR VOLUMES
For an irreducible character xh of the symmetric group S,#, indexed by the partition A, the immanant function d,, acting on an n X n matrix A = (u,~), is defined as d,(A) = Z:, t s, ,y\*(c~)rI:= la,CCij. Th e associated normalized immanant d, is defined as z\* = d,/x\*(identity) where identity is t
Estimates for the average value of a concave function are called Hadamard inequalities. If Lebesgue measure is replaced by a (signed) measure then it is still possible to get interesting and sharp inequalities. Here we extend these inequalities to log-concave functions.
Versions of the upper Hadamard inequality are developed for r-convex and r-concave functions.
In this note, we give a counterexample to show that Hadamard's inequality does not hold on a polyhedron in multi-dimensional Euclidean space. Then we give a sufficient condition on the polyhedron for Hadamard's inequality to hold. Finally, we provide an approach to create a large class of polyhedra