Prime power divisors of the number of n × n alternating sign matrices

Darrin D. Frey, James Allen Sellers

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We let A(n) equal the number of n × n alternating sign matrices. From the work of a variety of sources, we know that A(n) =∏ l=0 n-1(3l+1)!/(n+l)! We find an efficient method of determining ord p(A(n)), the highest power of p which divides A(n), for a given prime p and positive integer n, which allows us to efficiently compute the prime factorization of A(n). We then use our method to show that for any nonnegative integer k, and for any prime p > 3, there are infinitely many positive integers n such that ord p(A(n)) =k. We show a similar but weaker theorem for the prime p = 3, and note that the opposite is true for p = 2.

Original language English (US) 139-147 9 Ars Combinatoria 71 Published - Apr 2004

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Alternating Sign Matrices
Divisor
Integer
L'Hôpital's Rule
High Power
Divides
Non-negative
Theorem

All Science Journal Classification (ASJC) codes

• Mathematics(all)

Cite this

Frey, Darrin D. ; Sellers, James Allen. / Prime power divisors of the number of n × n alternating sign matrices. In: Ars Combinatoria. 2004 ; Vol. 71. pp. 139-147.
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Prime power divisors of the number of n × n alternating sign matrices. / Frey, Darrin D.; Sellers, James Allen.

In: Ars Combinatoria, Vol. 71, 04.2004, p. 139-147.

Research output: Contribution to journalArticle

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