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Hook immanantal inequalities for Laplacians of trees

✍ Scribed by Onn Chan; T.K. Lam

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
1013 KB
Volume
261
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

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 the identity permutation.

P.

πŸ“œ SIMILAR VOLUMES

Hook immanantal inequalities for trees e
Hook immanantal inequalities for trees explained
✍ Onn Chan; T.K. Lam πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 377 KB

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 Hadamar
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✍ Onn Chan; Bee-San Ng πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 124 KB

For an n Γ— 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