5 problems

Let $X_{(2,2,k)}^3$ be the no-three-way interaction model of two binary random variables and a third one with state space $k$. Its polar degrees form a sequence. Palindromicity con…

Let $\T_{a,b,d}$ be the trapezoid model in the simplex described above, with parameters $a$, $b$, and $d$, and let $D(\T_{a,b,d})$ denote its maximum divergence. Trapezoid-model di…

A staged tree model is a statistical model associated with a staged tree, and it has toric structure when its defining algebra can be represented as a toric algebra. The toric-stru…

Let $\mathcal{G}$ be a finite group acting on a finite set of states, and let $L$ be a labeling function that is symmetric and $\mathcal{G}$-compatible. A labeling is friendly when…

Bounded-loop conjecture. For each $S$, there exists an integer $k_S$ such that a Markov basis consists of moves that are sums of at most $k_S$ extended simple loops.