A precise description of the p-adic valuation of the number of alternating sign matrices
Clemens Heuberger, Helmut Prodinger
TL;DR
This paper derives an exact analytic expression for the p-adic valuation of the number of alternating sign matrices, revealing its fluctuating behavior through Fourier coefficients using Mellin-Perron analysis.
Contribution
It provides a novel, precise formula for v_p(T(N)) of alternating sign matrices, employing Fourier analysis and Mellin-Perron techniques.
Findings
Exact formula for v_p(T(N)) involving Fourier coefficients
Demonstrates fluctuating behavior of p-adic valuation
Utilizes Mellin-Perron method for analysis
Abstract
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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