Results 1  10
of
113
On ternary squarefree circular words
"... Circular words are cyclically ordered finite sequences of letters. We give a computerfree proof of the following result by Currie: squarefree circular words over the ternary alphabet exist for all lengths l except for 5, 7, 9, 10, 14, and 17. Our proof reveals an interesting connection between ter ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Circular words are cyclically ordered finite sequences of letters. We give a computerfree proof of the following result by Currie: squarefree circular words over the ternary alphabet exist for all lengths l except for 5, 7, 9, 10, 14, and 17. Our proof reveals an interesting connection between
Squarefree partial words
, 2008
"... We say that a partial word w over an alphabet A is squarefree if every factor xx ′ of w such that x and x ′ are compatible is either of the form ⋄a or a ⋄ where ⋄ is a hole and a ∈ A. We prove that there exist uncountably many squarefree partial words over a ternary alphabet with an infinite numbe ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
We say that a partial word w over an alphabet A is squarefree if every factor xx ′ of w such that x and x ′ are compatible is either of the form ⋄a or a ⋄ where ⋄ is a hole and a ∈ A. We prove that there exist uncountably many squarefree partial words over a ternary alphabet with an infinite
The Minimal Density of a Letter in an Infinite Ternary SquareFree Word is 883
"... The problem of determining the minimal density of a letter in an infinite ternary squarefree word was investigated by Tarannikov and Ochem. In this paper we solve this problem, and prove that the minimal density is equal to 883 3215. 1 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
The problem of determining the minimal density of a letter in an infinite ternary squarefree word was investigated by Tarannikov and Ochem. In this paper we solve this problem, and prove that the minimal density is equal to 883 3215. 1
Author manuscript, published in "WORDS 2007, France (2007)" Unequal letter frequencies in ternary squarefree words
, 2007
"... We consider the set S of triples (x,y, z) corresponding to the frequency of each alphabet letter in some infinite ternary squarefree word (so x + y +z = 1). We conjecture that this set is convex. We obtain bounds on S by with a generalization of our method to bound the extremal frequency of one let ..."
Abstract
 Add to MetaCart
We consider the set S of triples (x,y, z) corresponding to the frequency of each alphabet letter in some infinite ternary squarefree word (so x + y +z = 1). We conjecture that this set is convex. We obtain bounds on S by with a generalization of our method to bound the extremal frequency of one
Pagodas and Sackcloth: Ternary Sequences of Considerable Linear Complexity
, 1997
"... The zerosquare table, as an alternative to the established LCP notation for measuring the linear complexity of a qary sequence, offers a more readily applicable tool for investigating cipher keystreams. After a look at the classical problem of constructing powerfree sequences, we turn to the (ana ..."
Abstract
 Add to MetaCart
The zerosquare table, as an alternative to the established LCP notation for measuring the linear complexity of a qary sequence, offers a more readily applicable tool for investigating cipher keystreams. After a look at the classical problem of constructing powerfree sequences, we turn
The minimal density of a letter in an infinite . . .
, 2002
"... We study the minimal density of letters in infinite squarefree words. First, we give some definitions of minimal density in infinite words and prove their equivalence. Further, we propose a method that allows to strongly reduce an exhaustive search for obtaining lower bounds for minimal density. Ne ..."
Abstract
 Add to MetaCart
. Next, we develop a technique for constructing squarefree morphisms with extremely small density for one letter that gives upper bounds on the minimal density. As an application of our technique we prove that the minimal density of any letter in infinite ternary squarefree words is 0.2746... .
Ternary Expansions of Powers of 2
, 2007
"... P. Erdős asked how frequently 2 n has a ternary expansion that omits the digit 2. He conjectured this holds only for finitely many values of n. We generalize this question to consider iterates of two discrete dynamical systems. The first considers ternary expansions of real sequences xn(λ) = ⌊λ2 n ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
P. Erdős asked how frequently 2 n has a ternary expansion that omits the digit 2. He conjectured this holds only for finitely many values of n. We generalize this question to consider iterates of two discrete dynamical systems. The first considers ternary expansions of real sequences xn(λ) = ⌊λ2 n
unknown title
"... The minimal density of a letter in an infinite ternary squarefree word is 0.2746 · · · ..."
Abstract
 Add to MetaCart
The minimal density of a letter in an infinite ternary squarefree word is 0.2746 · · ·
Results 1  10
of
113