39 problems

Conjecture on oriented-graph speeds. This predicts a jump from polynomial to at least factorial speed for unlabelled hereditary properties of oriented graphs. The paper poses it as…

Conjecture on the possible bases.

No-accumulation-from-above conjecture. For every $c\in\mathbb{R}$, there exists $\varepsilon=\varepsilon(c)$ such that

Smallest-speed-above-2 conjecture. The smallest $c\in\mathcal{S}$ with $c>2$ is the largest real root of

Exponential growth-rate conjecture. The limit

Let $A_4$ be the Stanley sequence starting from the set $\{0,4\}$. Its growth rate is compared with the scale $n^2/\log n$. The conjecture for $A_4$. The sequence does not have gro…

Polynomial-growth conjecture. The total dimension satisfies

Perron-number conjecture. The growth rate of any Coxeter system of dimension at most $2$ is a Perron number.

Let $\pi_n\mathbb{S}$ denote the $n$th stable stem and let $\operatorname{rank}_p$ denote its rank at the prime $p$. Few-differentials conjecture. The stable stems satisfy … This c…

Let $X$ be a finite spectrum of type $h$, and let $\varpi_{\mathrm{T}(h)}(X,n)$ denote the size function measuring its telescopic homotopy groups through degree $n$. Telescopic gro…

For a real $b2>1$, let $b1'(k,b2)$ be the growth rate of the language of words containing no $b2$-power whose tail has length at most $2$. Stronger tail-restricted growth conjectur…

For any real $b2>1$, let $b1(k,b2)$ denote the growth rate of the language of $b2$-free words over an alphabet of size $k$. Shur's asymptotic growth conjecture. For every fixed int…

The alpha-primary growth conjecture. If $f(n)=O(c^n)$ for some $c<e^\alpha$, then $f$ is a polynomial.

For every $n\geq 2$, let $T_n$ be the threshold language of order $n$, and define its growth rate by … Since $T_n$ is factorial, this limsup can equivalently be replaced by a limit…

For every integer $n\geq 2$, let $A_n=\{\texttt{1},\texttt{2},\dots,\texttt{n}\}$ and let $T_n$ be the language of all $\operatorname{RT}(n)^+$-free words over $A_n$, where…

Simon's near-$2^n$ conjecture. Then $G$ is either $\operatorname{Aut}(S(2))$, or the group of automorphisms and anti-automorphisms of $S(2)$.

Generalized Fibonacci growth conjecture. If

Monadic NIP growth conjecture.

Let $G$ be a primitive oligomorphic permutation group acting on a countable infinite set … of size $n$. Macpherson's theorem states that there is a constant $c>1$ such that either…

Let $\mathcal{C}$ be a sum-closed permutation class, and let $\mathcal{C}^{\not\oplus}$ denote its indecomposable permutations. Linear indecomposable-count conjecture. If the seque…

Let $\mathcal{C}$ be a sum-closed permutation class, and let $\mathcal{C}^{\not\oplus}$ denote its indecomposable permutations. Define $\tau$ to be the unique positive root of … so…

Let $\mathcal{C}$ be a sum-closed and $rc$-invariant permutation class. Let $\operatorname{gr}(\mathcal{C})$ denote its growth rate and $\operatorname{gr}^{rc}(\mathcal{C})$ the gr…

Let $\mathcal{C}$ be a permutation class. Write $\overline{\operatorname{gr}}(\mathcal{C})$ for its upper growth rate and $\overline{\operatorname{gr}}^{rc}(\mathcal{C})$ for the u…

DLA superminimal growth conjecture.

DLA growth exponent conjecture. There exists $\tfrac{1}{d}<\alpha<1$ such that