4 problems

Constellation enumeration conjecture. The number of $m$-constellations having $n$ black faces is

Let $m$ be a positive integer. Consider greedy $m$-Tamari intervals whose maximal element has $n_i$ ascents of length $i$ for each $i\ge 1$, including a first ascent of length…

Let $k\geq 1$ and let $\lambda,\mu^0,\ldots,\mu^k$ be partitions of size $n\geq 1$. A connected rooted $k$-constellation with profile $(\lambda,\mu^0,\ldots,\mu^k)$ is denoted by…

Let $k\geq 1$ and let $\lambda,\mu^0,\ldots,\mu^k$ be partitions of size $n\geq 1$. Define $c^\lambda_{\mu^0,\ldots,\mu^k}(b)$ and $h^\lambda_{\mu^0,\ldots,\mu^k}(b)$ by the coeffi…