15 problems

Asymptotic growth constant conjecture. The asymptotic growth constant is

Spanning-tree factorization conjecture. The number of spanning trees is

Let $K$ be the Sierpiński gasket. For a nonconstant harmonic function $h$ on $K$, let $uh=muh/muh(K)$ be its normalized energy measure. For nonconstant harmonic functions $h1,h2$…

Bell–Ho–Strichartz conjecture. As $m\to\infty$, the law of $r\circ c^{(w)}$ under $\lambda_m$ converges to the Dirac measure at $\sqrt{8/75}$, while the law of…

Nonvanishing normal derivative conjecture. For every integer $t\geq 0$,

Let $G_\infty$ be the infinite Sierpinski gasket lattice, let $\mathcal{U}$ be the spectral-decimation map, and let $\mathcal{J}(\mathcal{U})$ denote its Julia set. For parameters…

Let $\mathsf{SG}$ be the Sierpinski gasket graph, let $\mathcal{B}_n$ be the graph-metric ball of radius $n$, and let $\mathcal{I}_{|\mathcal{B}_n|}$ be the internal DLA cluster fo…

Boundary-value decay conjecture. For $r\neq 1$ and $r\neq\frac{\sqrt{17}-3}{4}$,

The ratio-existence conjecture. For all but at most finitely many values of $r$,

The asymptotic ratio conjecture. For $r\neq \frac{\sqrt{17}-3}{4}$,

The asymptotic ratio conjecture. For $r\neq 1$ and $r\neq \frac{\sqrt{17}-3}{4}$,

Let $SG$ be the graphical Sierpinski gasket, let $o$ be its source vertex, and let $B_o(n)$ denote the graph-metric ball of radius $n$ centered at $o$. Write…

Let $\beta_m$ be the level-$m$ vertex set of the Sierpinski gasket, let $y$ be a non-boundary vertex in $\beta_m$, and let $\phi_y^{(m)}$ be the pointwise sampling function satisfy…

Let $\psi_m$ be a sampling function on level $m$ of the Sierpinski gasket $SG$. L2 decay conjecture. There is a constant $c$, numerically around $1.1$, such that … Unlike the corre…

Let $\psi_m$ denote a sampling function on level $m$ of the Sierpinski gasket. Uniform boundedness conjecture. The sampling functions are uniformly bounded by some constant, numeri…