3 problems

Let $P_n(x;\bm{\mu})$ be the row-generating polynomials of the Graham–Knuth–Patashnik recurrence, with parameters $\bm{\mu}=(\alpha,\beta,\gamma,\alpha',\beta',\gamma')$ treated as…

Coefficientwise Hankel-total positivity conjecture. The row-generating polynomials of $[\mathbf{JS}_{n,k}]_{0\leq k\leq n}$ are coefficientwise Hankel-totally positive in $(x,y,q)$…

Let $A_n(x)$ be the polynomial defined earlier in the paper, and let a sequence be infinite logconcave when every iterate of the operator $\mathfrak{L}$ produces a positive sequenc…