3 problems

Generalized Euler-number valuation conjecture. For $t\ge 1$, one has $\mu_{j,0,t}=0$, $\mu_{j,1,t}=4$, and, for $n>1$,

Let $k$ be a field, let $\{\mathbf e_i\}_{1\leq i\leq \ell}$ be the standard basis of $k^\ell$, and let $\mathbf B=(B_1,\ldots,B_\ell)$ be a delta $\ell$-tuple with…

Let $u$ be a parameter, let $hat{c}$ be the umbral operator used in the preceding identities, and let $varphi(0)$ denote its evaluation factor. Umbral interchange conjecture. The…