Zhao Shen

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math.CO2026

2-adic Valuations of Coefficients of the Fifth and Ninth Powers of the Thue--Morse Generating Function

Zhao Shen, Xinping Wang

Let $T (x) = \prod_{k = 0}^{\infty} (1 - x^{2^{k}})$ be the generating function of the Thue--Morse sequence, and write $T (x)^{m} = \sum_{n \geq 0} t_{m} (n) x^{n}$ . We prove exact formulas for the $2$ -a…

math.CO2026

Unboundedness of the Coefficients of Higher Powers of a Unimodular Power Series

Zhao Shen

Let $R (z) = \sum_{n = 0}^{\infty} r_{n} z^{n}$ be a power series with $∣ r_{n} ∣ = 1$ for every $n \geq 0$ . We show that for each integer $m \geq 2$ , the coefficient sequence of $R (z)^{m}$ is unbounde…