3 problems

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The degree conjecture for multivariate Prouhet–Thue–Morse polynomials
Degree conjecture. One has $\operatorname{deg}_{t}H_{m,n}(X,t)=m-1$ . In particular,
Conjectureopenfinite-differences polynomial-identities pouhet-thue-morsearXiv posted 2 days ago
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A generalized Prouhet–Thue–Morse divisibility conjecture
Generalized Prouhet–Thue–Morse divisibility conjecture. If $k=2$ , then
Conjectureopencombinatorial-identities polynomial-divisibility pouhet-thue-morsearXiv posted 2 days ago
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A generalized Prouhet–Thue–Morse identity for products of binary sums
The generalized Prouhet–Thue–Morse identity. One has
Conjectureopencombinatorial-identities polynomial-identities pouhet-thue-morsearXiv posted 2 days ago