We define an operation called transposition on words of fixed length. This operation arises naturally when the letters of a word are considered as entries of a matrix. Words that are invariant with respect to transposition are of special interest. It turns out that transposition invariant words have a simple interpretation by means of elementary group theory. This leads us to investigate some properties of the ring of integers modulo n and primitive roots. In particular, we show that there are infinitely many prime numbers p with a primitive root dividing p + 1 and infinitely many prime numbers p without a primitive root dividing p + 1. We also consider the orbit of a word under transposition.

Pappalardi, F., Saari, F., Lepisto, A. (2007). Transposition Invariant Words. THEORETICAL COMPUTER SCIENCE, 380, 377-387 [10.1016/j.tcs.2007.03.029].

Transposition Invariant Words

PAPPALARDI, FRANCESCO;
2007-01-01

Abstract

We define an operation called transposition on words of fixed length. This operation arises naturally when the letters of a word are considered as entries of a matrix. Words that are invariant with respect to transposition are of special interest. It turns out that transposition invariant words have a simple interpretation by means of elementary group theory. This leads us to investigate some properties of the ring of integers modulo n and primitive roots. In particular, we show that there are infinitely many prime numbers p with a primitive root dividing p + 1 and infinitely many prime numbers p without a primitive root dividing p + 1. We also consider the orbit of a word under transposition.
2007
Pappalardi, F., Saari, F., Lepisto, A. (2007). Transposition Invariant Words. THEORETICAL COMPUTER SCIENCE, 380, 377-387 [10.1016/j.tcs.2007.03.029].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/117440
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact