Power Values of Palindromes

Analyses of the Sequence and Structural Properties Corresponding to Pentapeptide and Large Palindromes in Proteins

The analyses of 3967 representative proteins selected from the Protein Data Bank revealed the presence of 2803 pentapeptide and large palindrome sequences with known secondary structure conformation. These represent 2014 unique palindrome sequences. 60% palindromes are not associated with any regular secondary structure and 28% are in helix conformation, 11% in strand conformation and 1% in the...

( 1 , k ) - Compositions

A (1, k)-composition of a positive integer n consists of an ordered sequence of the integers 1 and k whose sum is n. A palindromic (1, k)-composition is one for which the sequence is the same from left to right as from right to left. We give recursive equations and generating functions for the total number of such compositions and palindromes, and for the number of 1’s, k’s, “+”signs and summan...

Arnoux-rauzy Subshifts: Linear Recurrence, Powers, and Palindromes

N ov 2 00 7 Finite Automata , Palindromes , Patterns , and Borders

Given a language L and a nondeterministic finite automaton M , we consider whether we can determine efficiently (in the size of M) if M accepts at least one word in L, or infinitely many words. Given that M accepts at least one word in L, we consider how long the shortest word can be. The languages L that we examine include the palindromes, the non-palindromes, the k-powers, the non-k-powers, t...

Looking for All Palindromes in a String

A palindrome is a string of the form αα', where α and α' are also strings and reverse to each other. The problem of the paper is defined as follows: given a string S of length n, find all palindromes occurring in the given string S. In the paper, we present an algorithm based on suffix trees to find palindromes. Our algorithm will find all maximum palindromes which are not contained in any othe...