Affiliation:
1. Department of Mathematics and Statistics , University of Victoria , Victoria , BC, V8W 2Y2 , Canada
Abstract
Abstract
The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix B ∈ 𝔽
n×n
is defined as ℓ1ℓ2· · · ℓ
n
, where ℓ
j
∈ {A, S, N} according to whether all, some but not all, or none of the principal minors of order j of B are nonzero. Building upon the second author’s recent classification of the epr-sequences of symmetric matrices over the field 𝔽 = 𝔽2, we initiate a study of the case 𝔽= 𝔽3. Moreover, epr-sequences over finite fields are shown to have connections to Ramsey theory and coding theory.
Subject
Geometry and Topology,Algebra and Number Theory
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