14 problems

Three-factor radical-generation conjecture. The radical of $J_{p,3}$ is the prime ideal $I_{p,3}$:

Circular lexicographic delightfulness conjecture. The circular lexicographic term order is $2$-delightful for $I_{p,1}$. More specifically, the reduced Gröbner basis for $I_{p,2}$…

Two-factor minimal-generation conjecture. The ideal $I_{p,2}$ is minimally generated by

Linear-eliminant membership conjecture. If $m\geq 2$, $p\geq 2m+2$, and $R\cup C\neq\bar R\cup\bar C$, then

Finiteness conjecture for factor-analysis ideals. For arbitrarily many factors, the ideal is generated by polynomials arising from submatrices whose size depends on the number of f…

Two-factor generation conjecture. For two-factor models, the ideal $I_{p,2}$ is generated by the $3\times 3$-minors and pentads.

Tightness conjecture. The bound from Theorem bound-alternate is tight for all such $p$, $k$, and $r$; equivalently,

Knowns-and-unknowns sufficiency conjecture. Condition should be sufficient for identifiability in multi-channel factor analysis.

Shapiro's conjecture. The identifiability threshold that is generically sufficient for local identifiability should also be generically sufficient for global identifiability.

Thurstone's conjecture. Simple structure resolves the rotational invariance of factor analysis.

Jöreskog's equivalence conjecture. The first pair of conditions, C1 and C3, is equivalent to the displayed fixed-zero and fixed-nonzero-value condition, C.

Jöreskog's conjecture. These three conditions are sufficient for obtaining global rotational uniqueness.

Consider the distribution-free random factor analysis model with $p$ observed variables and $n$ observations, in the high-dimensional regime $p>n$. The method exhibits the describe…

Let $n$ and $m$ be the dimensions appearing in the model, let $c$ be the corresponding asymptotic aspect ratio, let $\boldsymbol{v}$ be the relevant eigenvector, let…