# On Combinatorial Generation of Prefix Normal Words

arXiv: https://arxiv.org/abs/1401.6346 · HTML: https://mlsanity.com/paper/1401.6346/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2014.

## Built on by (most cited first, 1 of 1)

- [Word Chain Generators for Prefix Normal Words](https://mlsanity.com/paper/2508.19619/) (2025)

## Abstract (arXiv)

A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present an efficient algorithm for exhaustively listing the prefix normal words with a fixed length. The algorithm is based on the fact that the language of prefix normal words is a bubble language, a class of binary languages with the property that, for any word w in the language, exchanging the first occurrence of 01 by 10 in w results in another word in the language. We prove that each prefix normal word is produced in O(n) amortized time, and conjecture, based on experimental evidence, that the true amortized running time is O(polylog(n)).