arXiv subjects

Edita Pelantová

Publications and source records attributed to Edita Pelantová.

75 records · Page 5Linked to original sources

arXiv2006

Factor versus palindromic complexity of uniformly recurrent infinite words

We study the relation between the palindromic and factor complexity of infinite words. We show that for uniformly recurrent words one has P(n)+P(n+1) \leq ΔC(n) + 2, for all n \in N. For a large class of words it is a better estimate of the palindromic complexity in terms of the factor complexity then the one presented by Allouche et al. We provide several examples of infinite words for which our estimate reaches its upper bound. In particular, we derive an explicit prescription for the palindromic complexity of infinite words coding r-interval exchange transformations. If the permutation πconnected with the transformation is given by π(k)=r+1-k for all k, then there is exactly one palindrome of every even length, and exactly r palindromes of every odd length.

math.CO↗

arXiv2006

Palindromic complexity of infinite words associated with simple Parry numbers

A simple Parry number is a real number β>1 such that the Rényi expansion of 1 is finite, of the form d_β(1)=t_1...t_m. We study the palindromic structure of infinite aperiodic words u_βthat are the fixed point of a substitution associated with a simple Parry number β. It is shown that the word u_βcontains infinitely many palindromes if and only if t_1=t_2= ... =t_{m-1} \geq t_m. Numbers βsatisfying this condition are the so-called confluent Pisot numbers. If t_m=1 then u_βis an Arnoux-Rauzy word. We show that if βis a confluent Pisot number then P(n+1)+ P(n) = C(n+1) - C(n)+ 2, where P(n) is the number of palindromes and C(n) is the number of factors of length n in u_β. We then give a complete description of the set of palindromes, its structure and properties.

math.CO↗

arXiv1999

s-convexity, model sets and their relation

The relation of s-convexity and sets modeling physical quasicrystals is explained for quasicrystals related to quadratic unitary Pisot numbers. We show that 1-dimensional model sets may be characterized by s-convexity for finite set of parameters s. It is shown that the three Pisot numbers $\frac12(1+\sqrt5)$, $1+\sqrt2$, and $2+\sqrt3$ related to experimentally observed non-crystallographic symmetries are exceptional with respect to s-convexity.

math.RA↗