Classification of families of pr- and 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 $3$.