A precise description of the p-adic valuation of the number of alternating sign matrices

Details A precise description of the p-adic valuation of the number of alternating sign matrices A precise description of the p-adic valuation of the number of alternating sign matrices

2009-08-03

arxiv.org/abs/0908.0149v1

Int. J. Number Theory 7 (2011), 57-69

Mathematics

Number Theory

Scientific paper

10.1142/S1793042111003892

Following Sun and Moll, we study v_p(T(N)), the p-adic valuation of the
counting function of the alternating sign matrices. We find an exact analytic
expression for it that exhibits the fluctuating behaviour, by means of Fourier
coefficients. The method is the Mellin-Perron technique, which is familiar in
the analysis of the sum-of-digits function and related quantities.

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