The total run length of a word
A run in a word is a periodic factor whose length is at least twice its period and which cannot be extended to the left or right (by a letter) to a factor with greater period. In recent years a great deal of work has been done on estimating the maximum number of runs that can occur in a word of leng...
| Main Authors: | , |
|---|---|
| Format: | Journal Article |
| Published: |
Elsevier
2013
|
| Online Access: | http://hdl.handle.net/20.500.11937/42452 |
| Summary: | A run in a word is a periodic factor whose length is at least twice its period and which cannot be extended to the left or right (by a letter) to a factor with greater period. In recent years a great deal of work has been done on estimating the maximum number of runs that can occur in a word of length n. A number of associated problems have also been investigated. In this paper we consider a new variation on the theme. We say that the total run length (TRL) of a word is the sum of the lengths of the runs in the word and that τ(n) is the maximum TRL over all words of length n. We show that n2/8<τ(n)<47n2/72+2nn2/8<τ(n)<47n2/72+2n for all n. We also give a formula for the average total run length of words of length n over an alphabet of size α, and some other results. |
|---|