9 problems

Let $[n]=\{1,\ldots,n\}$, let $\beta$ be the restriction function on $[2]\times[b]$ defined by … and let $\mathcal{L}_{([2]\times[b])\times[\ell]}(R^{\beta})$ denote the correspond…

Let $V=\{a,b,c\}$ be the three-element poset with $a\lessdot b$ and $a\lessdot c$, let $\mathcal{L}_{V\times[\ell]}(R^q)$ denote the set of $V$-strict labelings with restriction fu…

Let $V=\{a,b,c\}$ be the three-element poset with $a\lessdot b$ and $a\lessdot c$, let $\mathcal{A}^{\ell}(P)$ denote the set of $P$-partitions of height $\ell$, and let…

Let $\mathcal{L}_{P\times[\ell]}(R^q)$ denote the set of labelings with the stated restriction function, and let $\xi$ be the statistic defined in the preceding formulation. Transl…

Let $\mathcal{L}_{P \times [\ell]}(R^q)$ denote the set of labelings subject to the indicated restriction function, let $\xi(f,(x_1,x_2),b)$ be the statistic defined by … and let…

Let $[n]=\{1,\ldots,n\}$, let $\mathcal{A}^2(P)$ denote the set of $P$-partitions of height at most $2$, and let $\chi_S$ be the indicator statistic of $S$. For antipodal elements…

Birational OY-invariant conjecture. The function $\EuScript{Y}^{\mathrm{B}}\colon\mathcal{A}^{\mathrm{B}}(\mathsf{A}^n)\to\mathbb{R}_{>0}$ is invariant under both…

Birational type B homomesy conjecture. The statistics $h^{\mathrm{B}}_i\colon \mathcal{A}^{\mathrm{B}}_{\kappa}(\mathsf{B}^n)\to \mathbb{R}_{>0}$, for $1\leq i\leq 2n-1$, and…

The type B piecewise-linear homomesy conjecture. The statistic $h^{\mathrm{PL}}_*\colon \mathcal{A}^{\mathrm{PL}}_{\kappa}(\mathsf{B}^n)\to \mathbb{R}$ is $\kappa$-mesic for…