9 problems

Let $C$ denote the set of small conditionals, let $J-1$ be the dimension of the underlying lattice, and consider the coefficient matrix of the Diophantine equation governing the ma…

Contingency-table norm conjecture. For arbitrary table dimensions $m$ and $n$, table sum $\Sigma$, and row and column sums $r_k$ and $c_p$, this multi-decomposition is non-degenera…

Logarithmic maximum-entry conjecture. With high probability,

Let $\mathbf d=(d_1,\ldots,d_n)\in\mathbb N^n$ satisfy $0\le d_i\le n-1$, and let $c(\mathbf d)$ be the number of simple graphs on vertices $v_1,\ldots,v_n$ with $\deg(v_i)=d_i$ fo…

Let $\mathbf a\in\mathbb N^r$ and $\mathbf b\in\mathbb N^s$ have common size $n=|\mathbf a|=|\mathbf b|$, and let $\operatorname{CT}(\mathbf a,\mathbf b)$ be the number of continge…

Let $p_{ijk\ell}$ be entries of a $2\times2\times2\times2$ table sampled uniformly from the probability simplex, with $i,j,k,\ell\in\{0,1\}$ and $p_{ijk\ell}\geq0$. Consider the tw…

Let $M$ be the matrix in the equation defining the space of tables, and let $A$, $B$, and $C$ denote the index sets used to specify the table and its conditionals. A total Markov b…

Let $m$ covariates index combinations of levels, and let ${\cal B}_{\Lambda(A_1 \otimes \dots \otimes A_m)}$ be the set of moves … Consider the subset for which every element of…

Let $m$ covariates index combinations of levels, and let $\Bj=(j_1,\dots,j_m)$ denote such a combination. Let $\bm{e}_{\Bj}$ be the array with $1$ at cell $(1,\Bj)$ and $-1$ at cel…