### 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) |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

- Language and Linguistics
- Linguistics and Language

### Cite this

*Journal of Quantitative Linguistics*,

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

}

*Journal of Quantitative Linguistics*, vol. 13, no. 1, pp. 45-55. https://doi.org/10.1080/09296170500500777

**Improving calculations of the number of distinct alignments of two strings.** / Rødseth, Øystein J.; Sellers, James A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Improving calculations of the number of distinct alignments of two strings

AU - Rødseth, Øystein J.

AU - Sellers, James A.

PY - 2006/12/1

Y1 - 2006/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=43249154408&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43249154408&partnerID=8YFLogxK

U2 - 10.1080/09296170500500777

DO - 10.1080/09296170500500777

M3 - Article

AN - SCOPUS:43249154408

VL - 13

SP - 45

EP - 55

JO - Journal of Quantitative Linguistics

JF - Journal of Quantitative Linguistics

SN - 0929-6174

IS - 1

ER -