### Abstract

In a recent work, Covington discusses the enumeration of two different sets of alignments of two strings of symbols using elementary combinatorial techniques. He defines two functions a(m, n) and A(m, n) to count the number of two-string alignments in his "small" and "middle" sets of alignments (respectively). He provides a recurrence for each of these functions which allows for the calculation of values of a(m,n) and A(m,n). In this note, we obtain generating functions for each of these functions. With the generating functions in hand, we provide improvements on Covington's recurrences, making the calculation of a(m, n) and A(m, n) much more efficient.

Original language | English (US) |
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Pages (from-to) | 45-55 |

Number of pages | 11 |

Journal | Journal of Quantitative Linguistics |

Volume | 13 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 2006 |

### All Science Journal Classification (ASJC) codes

- Language and Linguistics
- Linguistics and Language

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## Cite this

Rødseth, Ø. J., & Sellers, J. A. (2006). Improving calculations of the number of distinct alignments of two strings.

*Journal of Quantitative Linguistics*,*13*(1), 45-55. https://doi.org/10.1080/09296170500500777