Home»Definitions» Equidistant Letter Sequence ELS

# Equidistant Letter Sequence ELS

An equidistant letter sequence, called ELS for short, is a sequence of equally spaced letters in the text not counting spaces and punctuation marks. The sequence of the letter positions form an arithmetic progression.

Several properties associated with an ELS e are:
• B(e): the beginning position of ELS e
• E(e): the ending position of ELS e
• L(e): the number of characters in ELS e
• S(e): the skip of ELS e
• W(e): the character string W(e)1, ..., W(e)L(e)> of ELS e

These properties have two constraints: B(e) < E(e) and the relation binding the end position to the beginning position

E(e)=B(e)+(L(e)-1)|S(e)|

The positions determined by the ELS e are given by B(e), B(e)+|S(e)|, ..., B(e)+(L(e)-1)|S(e)|.

For any i, i=1, ...,L(e), the ith character, W(e)i, of ELS e is associated with position B(e)+(i-1)|S(e)|.

The span of an ELS e is given by E(e)-B(e)+1 = 1+(L(e)-1)|S(e)|.

ELS e is said to be an ELS of key word w when w = W(e).

The skip S(e) of ELS e can be positive or negative depending on whether the ELS positions match in a forwards or backwards order. We call the first kind of ELS a positive skip ELS and the second kind of ELS a negative skip ELS.

ELS e is said to be a positive skip ELS of a word w whose respective characters are w1, ... , wLw if and only if

Lw=L(e) and wi = W(e)i, i=1, ... ,Lw.

ELS e is said to be a negative skip ELS of a word w whose respective characters are w1, ..., wLw if and only if

Lw=L(e) and wi = W(e)Lw+1-i, i = 1, ..., Lw

An ELS e is said to be an ELS of a word w in a text T if and only if it is an ELS of word w and

 TB(e)+iS(e) = wi+1, i = 0,..., L(e)-1 when S(e) > 0 and TB(e)+iS(e) = wL(e)-i, i = 0,..., L(e)-1 when S(e) < 0

The set of all ELSs E associated with a word w = ( w1, ..., w K and text T is given by

 E(w, T) = { e | TB(e)+iS(e) = wi+1 = W(e)i+1, i = 0,..., K-1,when S(e) > 0 ; TB(e)-iS(e) = wK-i = W(e)K-i, i = 0,..., K-1, when S(e) < 0 }

If we want to name the set of ELSs for a key word w in a text T with respect to a general skip specification σ, we will write E(w,T,σ).