16 problems

Let $\mathcal{C}$ be a permutation class. It is strongly algebraic if $\mathcal{C}$ and every subclass of $\mathcal{C}$ have algebraic generating functions, and it is well-quasi-or…

Let $M$ be a partial multiplication matrix, meaning a matrix whose nonzero entries are monotone classes, and suppose its cell graph is cyclic. Let $\mathcal X$ be a permutation cla…

A monotone grid class is a permutation class defined by a finite grid whose nonempty cells contain monotone permutations. Huczynska–Vatter's conjecture. Every monotone grid class i…

Let $\mathcal{C}$ be a permutation class, and let $\langle\mathcal{C}\rangle$ denote its substitution closure. The substitution-closure conjecture. If $\langle\mathcal{C}\rangle$ i…

Let $\mathcal{C}$ be a permutation class, and let $\mathcal{C}^{+1}$ denote its one-point extension. The 2-wqo one-point-extension conjecture. If $\mathcal{C}$ is 2-wqo, then…

Let $\mathcal{C}$ be a permutation class, and let $\mathcal{C}^{+1}$ denote its one-point extension. A class is lwqo when it is well-quasi-ordered under labeling by arbitrary wqo l…

For a permutation class $\mathcal{C}$ and an integer $n\geq 1$, say that $\mathcal{C}$ is $n$-well-quasi-ordered (or $n$-wqo) if the set of permutations in $\mathcal{C}$ labeled by…

Geometric griddability and finite-letter-graph conjecture. $X$ is geometrically griddable if and only if ${\cal G}_X$ is a class of $k$-letter graphs for some finite value of $k$.

Let an upper growth rate of a permutation class mean a real number that occurs as the upper exponential growth rate of that class, and let a sum closed class be a permutation class…

Deflatability conjecture. The class $\operatorname{Av}(pi)$ is deflatable.

Finite-basis conjecture for monotone grid classes. Every monotone grid class has a finite basis. The source notes that only limited cases are known, including skew-merged permutati…

Atkinson's conjecture.

Strongly algebraic characterization conjecture. A permutation class is strongly algebraic if and only if it is wpo. The source proves that every strongly algebraic class is wpo and…

A permutation class $\mathcal{C}$ is broadly rational if every finitely based subclass of $\mathcal{C}$ has a rational generating function, and it is strongly rational if it and al…

Let $\xi\approx 2.30524$ be the unique positive root of $x^5-2x^4-x^2-x-1$, and let the accumulation points from above of a set of real numbers be limits approached by larger eleme…

Let $\lambda$ be the unique real root of $x^5-2x^4-2x^2-2x-1$, and let $S$ be the set of growth rates of permutation classes that are below $\lambda$. Nowhere-dense growth-rate con…