37 problems

Monotonicity conjecture. The sequence

Let $\mathfrak{S}_n^t$ be the set of permutations of length $n$ that become the identity after $t$ applications of the stack-sorting operation, and let $\mathfrak{S}_n^t(p)$ denote…

Let $t\geq 1$, $n\geq 0$, and $p\in\{213,321\}$. A permutation is $t$-stack-sortable if it can be sorted using $t$ applications of the stack-sorting operator, and it avoids a patte…

Let a permutation be sortable by two stacks in series under the restriction that the permutation on the first stack avoids the classical pattern $1324$. Let $\operatorname{Av}(P)$…

Let $\text{SC}_{\underline{23}1}$ be the vincular-pattern-avoiding stack-sorting map, let $\text{Sort}_n(\text{SC}_{\underline{23}1})$ denote its sorting class in $\mathfrak S_n$,…

Let $\mathfrak S_n$ be the set of permutations of length $n$, and let $\text{SC}_{1\underline{23}}$ and $\text{SC}_{3\underline{21}}$ be the corresponding vincular-pattern-avoiding…

Let $\mathfrak S_n$ be the set of permutations of length $n$, and let $\text{SC}_{1\underline{23}}$ and $\text{SC}_{3\underline{21}}$ be the corresponding vincular-pattern-avoiding…

Let $\mathfrak S_n$ be the set of permutations of length $n$, and let $\text{SC}_{1\underline{23}}$ be the vincular-pattern-avoiding stack-sorting map. Second-largest-preimage conj…

Let $\text{SC}_{312}$, $\text{SC}_{\underline{31}2}$, and $\text{SC}_{3\underline{12}}$ be the vincular-pattern-avoiding stack-sorting maps, and let $\text{Sort}_n(f)$ denote the p…

For positive integers $t$ and $n$, let $\operatorname{Sort}_{t,n}(123,132)$ be the set of length-$n$ permutations that are $t$-stack-sortable under $s_{123,132}$. Enumerative recur…

Let $\mathfrak{M}_n$ be the set of minimally-sorted permutations under $s_{123,132}$. Enumerative conjecture. For every positive integer $n$, … This gives a recurrence between the…

Let $S_n$ be the set of permutations of length $n$. For a pair of patterns $(\sigma,\tau)$, let $s_{\sigma,\tau}:S_n\to S_n$ denote the corresponding generalized stack-sorting map,…

Let $S_n$ be the set of permutations of length $n$, let $SC_{231}:S_n\to S_n$ be the stack-sorting map whose stack avoids consecutive occurrences of $231$, and let…

Let $\mathcal D_n$ be the average number of iterations of the ordinary stack-sorting map $\operatorname{\mathtt{s}}$ needed to send an element of $S_n$ to the identity permutation,…

Let $B_n$ be the type-$B$ Coxeter group and let $\operatorname{\mathtt{s}}_B:B_n\to B_n$ be the type-$B$ stack-sorting map. For $v\in B_n$, write…

For a positive integer $n$, define the Narayana polynomial … Given a composition $\mathbf q=(q_0,\ldots,q_k)\in\mathbb Z_{>0}^{k+1}$, define … An integral binary nestohedron…

operatorname{SC}{132} image conjecture. If $\tau\in S_n$ satisfies

Universal fertility conjecture. For every $\sigma\in S_3$ and every positive integer $f$, there exists a permutation $\pi$ such that

Stabilization-time conjecture. For every $\pi\in S_n$,

Periodic-point avoidance conjecture. The periodic points of $\operatorname{SC}_\sigma$ are precisely the permutations in

Let $S_n$ be the set of permutations of length $n$, and let $s_{\{132,213\}}$ and $s_{\{231,213\}}$ be the corresponding stack-sorting maps. A permutation is periodic if some posit…

Central limit conjecture. The sequence $(Y_n)_{n\geq 1}$ converges in distribution to a random variable $Y$ such that

Let $\operatorname{revstack}=s\circ\operatorname{rev}$, where $s$ is the stack-sorting map and $\operatorname{rev}$ reverses a permutation. For a permutation $\sigma\in S_n$, let…

Let $\mathcal D_n$ be the average number of iterations of the stack-sorting map needed to sort a permutation in $S_n$ into the identity permutation. Strengthened West conjecture. T…

Stack-sorting growth conjecture. The value of this limit lies in the interval $(1.68,1.73)$.