TY - JOUR

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

AU - Rødseth, Øystein J.

AU - Sellers, James A.

PY - 2006

Y1 - 2006

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.

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U2 - 10.1080/09296170500500777

DO - 10.1080/09296170500500777

M3 - Article

AN - SCOPUS:43249154408

SN - 0929-6174

VL - 13

SP - 45

EP - 55

JO - Journal of Quantitative Linguistics

JF - Journal of Quantitative Linguistics

IS - 1

ER -