Classification of families of pr- and epr-sequences

TL;DR

This paper introduces new restrictions on attainable epr-sequences and classifies two families of sequences related to real symmetric matrices, focusing on patterns of principal rank characteristic sequences and enhanced sequences.

Contribution

It provides the first classification of pr-sequences without three consecutive ones and epr-sequences with an N in every length-3 subsequence, based on new restrictions.

Findings

Classified pr-sequences without three consecutive 1s.

Classified epr-sequences with an N in every length-3 subsequence.

Established new restrictions for attainable epr-sequences.

Abstract

This paper establishes new restrictions for attainable enhanced principal rank characteristic sequences (epr-sequences). These results are then used to classify two related families of sequences that are attainable by a real symmetric matrix: the family of principal rank characteristic sequences (pr-sequences) not containing three consecutive $1$s and the family of epr-sequences which contain an $\tt{N}$ in every subsequence of length $3$.