2 problems

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Guo–Zeng's odd ballot-number power divisibility conjecture
Let $A_{n,k}$ be the ballot numbers … For all $r\in\mathbb{N}$ and $n,s\in\mathbb{Z}^+$ such that $r+s\equiv 1\pmod 2$ , and with $\varepsilon=\pm1$ , Guo–Zeng's ballot-number divisi…
Conjectureopenballot-numbers binomial-congruences integer-sequencesarXiv posted 2 days ago
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The positive-coefficient numerator conjecture for Carlitz-Riordan polynomial interpolation
Positive-coefficient numerator conjecture. One can write
Conjectureopenballot-numbers polynomial-interpolation q-seriesarXiv posted 2 days ago

Guo–Zeng's odd ballot-number power divisibility conjecture