NDLI: Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields

Content Provider	Scilit
Author	Dukes, Peter J. Martínez-Rivera, Xavier
Copyright Year	2021
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.
Related Links	https://www.degruyter.com/document/doi/10.1515/spma-2021-0154/pdf
Ending Page	179
Page Count	14
Starting Page	166
e-ISSN	23007451
DOI	10.1515/spma-2021-0154
Journal	Special Matrices
Issue Number	1
Volume Number	10
Language	English
Publisher	Walter de Gruyter GmbH
Publisher Date	2021-12-30
Access Restriction	Open
Subject Keyword	Special Matrices Principal Minor Symmetric Matrix Finite Field Enhanced Principal Rank Characteristic Sequence Rank Journal: Special Matrices, Vol- 10
Content Type	Text
Resource Type	Article

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Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields