4 problems

Let $\Delta$ be a simplicial complex on $[n]$, with Stanley–Reisner ideal $I_\Delta$. Let $\Delta^s$, $\Delta^e$, and $\Delta^c$ denote its symmetric algebraic, exterior algebraic,…

Tomon’s conjecture. If $\mathcal H\subset\mathcal F_i^t(r)$, then

Symmetric and exterior shifting conjecture. If $\mathcal{S}$ is either the symmetric or exterior shifting operation, then $(\mathcal{S}(\Delta_n))_{n\ge 1}$ is also…

Symmetric shifting conjecture. If $(\Delta_n)_{n\ge 1}$ is an $\operatorname{Inc}$-invariant chain, then the chain $(\mathcal{S}(\Delta_n))_{n\ge 1}$ is $\operatorname{Inc}$-invari…