9 problems

Narayana refinement conjecture. The number $D_{nk}$ is divisible by

Narayana transformation conjecture. The Narayana transformation preserves log-convexity. The source presents this as a problem following known log-convexity results for specializat…

Sulanke's conjecture. On $\operatorname{SYT}(n^3)$, each of the statistics $\st_1$ and $\st_2$ has a $3$-Narayana distribution.

Bennett–Carrillo–Machacek–Sagan's conjecture. The generalized Narayana numbers $N_{\{n\,k\}}$ are positive integers for $n\geq1$. This conjecture concerns the integrality and posit…

Fuss–Narayana conjecture. For any $m\geq 1$, the Fuss–Narayana triangles are totally positive and the Fuss–Narayana squares are strictly totally positive. The source introduces thi…

Let $NA(n,k)=\frac{1}{k+1}\binom{n+1}{k}\binom{n}{k}$ be the Narayana numbers, and let … be the Narayana triangle of type $A$. Chen–Liang–Wang's conjecture. The Narayana triangle…

Total positivity conjecture. The Narayana triangle $N$ is totally positive: every minor of $N$ is nonnegative.

Let $N(n,m;k\mid 1)$ denote the rectangular Narayana numbers, indexed by $0\le k\le (n-1)(m-1)$. The sequence is symmetric about its midpoint. Rectangular Narayana unimodality conj…

Let $N(n,k)=\frac{1}{n}\binom{n}{k}\binom{n}{k+1}$ be the Narayana numbers. For a sequence $(a_k)_{k\geq 0}$ of positive real numbers, define its Narayana transform by … A sequence…