5 problems

For $n\geq1$ and $S\subseteq[n]$, let $\operatorname{Pin}(\pi)$ be the set of values at peak positions of $\pi\in\mathfrak{S}_n$, and define … A polynomial is $\gamma$-positive wit…

Let $T(n,k)$ be the sequence defined by … and, for $0<k<n$, … For each positive integer $n$, let $\mathsf{APS}^B_n$ denote the set of admissible pinnacle sets for signed permutatio…

Forest factorization conjecture. It was conjectured that

Let $F=(O,T_2,T_3,\dots,T_r)$ be a sequence of trees encoding a pinnacle set, where $O$ is the one-node tree, and let $p_n(F)$ denote the corresponding enumeration. Forest factoriz…

For a finite set $S$ of pinnacle values, let … Write $S=\{s_1,\dots,s_p\}$ with $n\geq s_p$, define … and set … Define abstract expressions by $E_1=x_{1,3}+x_{1,1}$,…