Journal of Integer Sequences, Vol. 14 (2011), Article 11.8.7

The p-adic Valuation of the ASM Numbers

Erin Beyerstedt and Victor H. Moll
Department of Mathematics
Tulane University
New Orleans, LA 70118

Xinyu Sun
Department of Mathematics
Xavier University of Louisiana
New Orleans, LA 70125


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.

Full version:  pdf,    dvi,    ps,    latex    

(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.

Return to Journal of Integer Sequences home page