The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Currently displaying 1 – 4 of 4

Showing per page

Order by Relevance | Title | Year of publication

Balances and Abelian Complexity of a Certain Class of Infinite Ternary Words

Ondřej Turek — 2010

RAIRO - Theoretical Informatics and Applications

A word defined over an alphabet 𝒜 is -balanced ( ) if for all pairs of factors , of of the same length and for all letters 𝒜 , the difference between the number of letters in and is less or equal to . In this paper we consider a ternary alphabet 𝒜 = {, , } and a class of substitutions ϕ p defined by ϕ p () = , ϕ p () = , ϕ p () = where 1. We prove that the fixed point of ϕ p , formally written as ϕ p (), is 3-balanced and that...

Balance properties of the fixed point of the substitution associated to quadratic simple Pisot numbers

Ondřej Turek — 2007

RAIRO - Theoretical Informatics and Applications

In this paper we will deal with the balance properties of the infinite binary words associated to -integers when is a quadratic simple Pisot number. Those words are the fixed points of the morphisms of the type ϕ ( A ) = A p B , ϕ ( B ) = A q for p , q , p q , where β = p + p 2 + 4 q 2 . We will prove that such word is -balanced with t = 1 + ( p - 1 ) / ( p + 1 - q ) . Finally, in the case that it is known [B. Adamczewski, (2002) 197–224] that the fixed point of the substitution ϕ ( A ) = A p B , ϕ ( B ) = A q is not -balanced for any . We exhibit an infinite sequence of pairs of words...

Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers

Lubomíra BalkováEdita PelantováOndřej Turek — 2007

RAIRO - Theoretical Informatics and Applications

We study some arithmetical and combinatorial properties of -integers for being the larger root of the equation . We determine with the accuracy of 1 the maximal number of -fractional positions, which may arise as a result of addition of two -integers. For the infinite word coding distances between the consecutive -integers, we determine precisely also the balance. The word is the only fixed point of the morphism → and → . In the case , the corresponding infinite word is sturmian, and, therefore,...

Circulant matrices with orthogonal rows and off-diagonal entries of absolute value 1

Daniel Uzcátegui ContrerasDardo GoyenecheOndřej TurekZuzana Václavíková — 2021

Communications in Mathematics

It is known that a real symmetric circulant matrix with diagonal entries d 0 , off-diagonal entries ± 1 and orthogonal rows exists only of order 2 d + 2 (and trivially of order 1 ) [Turek and Goyeneche 2019]. In this paper we consider a complex Hermitian analogy of those matrices. That is, we study the existence and construction of Hermitian circulant matrices having orthogonal rows, diagonal entries d 0 and any complex entries of absolute value 1 off the diagonal. As a particular case, we consider matrices whose...

Page 1

Download Results (CSV)