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