4 problems

Let $\mathscr{R}_n$ be the lecture hall cone in the special case associated with $(1,2,\ldots,n)$, let $\mathfrak{S}_{n-1}$ be the symmetric group, and let $\mathrm{des}(\pi)$ deno…

Recursive term-order conjecture. For this choice of term order, the recursive Gröbner basis conjecture for $I_n$ is true.

Recursive Gröbner basis conjecture. There exists a term order for which the Gröbner basis for $I_n$ contains all Gröbner basis elements from the Gröbner basis for $I_{n-1}$. It als…

Lecture-hall Sperner conjecture. There exists a regular, flag, unimodular triangulation of $R_n$ that admits a shelling order such that the maximal simplices of the triangulation a…