A PRECISE DESCRIPTION OF THE p-ADIC VALUATION OF THE NUMBER OF ALTERNATING SIGN MATRICES

作者：Heuberger Clemens^*; Prodinger Helmut

来源：International Journal of Number Theory, 2011, 7(1): 57-69.

DOI：10.1142/S1793042111003892

• Alternating sign matrices
• p-adic valuation
• sum-of-digits
• Mellin-Perron formula
• periodic fluctuation
• Fourier coefficients
• asymptotic expansion

Following Sun and Moll ([4]), 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 behavior, 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.

• 出版日期2011-2