6 problems

Let $K(n,k,l)$ be the recursively defined array of integers associated with the pascalized coupled Young graph, with $n\geq 3$, $k,l$ satisfying $2k+l<n-2$ and…

Let $\Theta$ be the coupled Young graph, let $\mathcal{P}(\Theta)$ be its pascalization, and let $A_{(\mathcal{C}_H,\delta)}(\infty)$ be the associated inductive limit algebra at t…

Let $\Theta$ be the coupled Young graph and let $\mathcal{P}(\Theta)$ be its pascalization. A central measure is a central measure on the space of infinite paths of this branching…

Let $A_{(\mathcal{H},\delta)}(\infty)$ be the inductive limit algebra associated with the hyperoctahedral case, and let its branching graph be the pascalization of the relevant pri…

The two-parameter processes $\operatorname{PDIPE}(\alpha,\theta)$ are diffusions on the boundary of the branching graph of integer compositions. An up-down chain on this graph adds…

Young-bouquet process conjecture. A similar construction can be carried out for the Young bouquet, yielding a Markov process whose dynamics are piecewise deterministic, meaning tha…