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The ***p*-adic Valuation of the ASM Numbers

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Erin Beyerstedt and Victor H. Moll

Department of Mathematics

Tulane University

New Orleans, LA 70118

USA

Xinyu Sun

Department of Mathematics

Xavier University of Louisiana

New Orleans, LA 70125

USA

**Abstract:**

A classical formula of Legendre gives the *p*-adic valuation for factorials
as a finite sum of values of the floor function. This expression can be
used to produce a formula for the *p*-adic valuation of *n* as a finite
sum of periodic functions. An analogous result is established for the
*p*-adic valuation of the ASM
numbers. This sequence counts the number of
alternating sign matrices.

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(Concerned with sequence
A005130.)

Received February 3 2011;
revised version received July 18 2011; September 8 2011.
Published in *Journal of Integer Sequences*, October 16 2011.

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