22 problems

Let $P$ be a poset with $n$ elements. A labeling of $P$ is tangled if it requires $n-1$ applications of extended promotion to become a natural labeling. Defant–Kravitz conjecture.…

Promotion conjecture. Theorem 4.11 remains true for any tensor product

Quasipolynomial divisibility conjecture. For every fixed tableau $T$, there exists a quasipolynomial in $n$ such that, for $n$ sufficiently large, the orbit length of $T[n]$ always…

Let $P$ be a poset with $n$ elements. Let $\Lambda(P)$ denote the set of labelings of $P$, let $L_{n-3}$ denote the relevant position in a labeling $L$, and let $\mathcal{L}(P)$ de…

Let $P$ be a poset with $n obreaktext{ elements}$, where $nge 2$. For each $xin P$, let $mathcal{T}x(P)$ be the set of tangled labelings of $P$ in which $x$ receives label $n-1$. *…

Let $P$ be a poset with $n$ elements, and let $a_k(P)$ be the number of labelings of $P$ requiring exactly $k$ applications of extended promotion to become a natural labeling. Unim…

Let $P$ be a poset with $n$ elements and $m$ minimal elements. A labeling of $P$ is tangled if it requires $n-1$ applications of extended promotion to become a natural labeling. Ho…

Late non-order-ideal labeling bound. The number of labelings $L:P\to[n]$ such that $L_{n-3}\notin\mathcal{L}(P)$ is at most

Tangled–quasi-tangled inequality. The number of tangled labelings of $P$ is less than or equal to the number of quasi-tangled labelings of $P$.

Coloring probability conjecture.

Refined tangled-labeling bound. $P$ has at most

Maximum noninvertibility conjecture. For any poset $P$,

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 $\mathcal{L}_{P\times[\ell]}(R^q)$ 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…

Dilks–Pechenik–Striker's order conjecture. The order of $K$-promotion on ${\mathrm{Inc}}^q(d^3)$ is exactly $q$.

Let $V(n)$ be the poset in the source, let $\mathcal{L}(V(n))$ denote its set of linear extensions, and let $\operatorname{Pro}$ denote promotion. Hopkins–Rubey's conjecture. For e…

Evacuation fixed-point conjecture. For all $n\geq 1$, the number of Kreweras words of length $3n$ satisfying $\operatorname{{Evac}}^{*}(w)=w$ is

A standard skew tableau has rows whose sizes weakly decrease from top to bottom; write $b$ for the number of rows and let $\stab$ denote its stabilization time, the least $k$ at wh…

Assume there is a bijection between generalized oscillating tableaux of length $k$ with $n$ parts, whose final component is $(m,\ldots,m)$ for some $m\in\mathbb{Z}$, and…

Periodicity conjecture. For every $T \in \operatorname{Inc}^q(3 \times n)$,