We classify the exact evaluation of $\operatorname{Holant}(f\mid=_3)$ for every fixed complex algebraic symmetric Boolean ternary signature $f$. An input is a cubic bipartite multigraph: every vertex on one side carries $f$, every vertex on the other side carries ternary equality, and no auxiliary signatures are freely...
We study Yang's higher numerical invariants for the quasi-homogeneous submodules \[ M_{k,\ell}=[z^k-w^\ell]\subset H^2(\mathbb D^2), \qquad k,\ell\in\mathbb N,\quad k\neq\ell. \] The Hilbert--Schmidt property and the low-order invariants $\Sigma_0$ and $\Sigma_1$ for this family follow from earlier results on $M_{\thet...
For $k\ge 2$, let $M_k=[z^k-w^k]$ be the principal homogeneous submodule of the Hardy space over the bidisk. We determine Yang's complete sequence of numerical invariants and prove $$ \Sigma_0(M_k)=\frac{\pi^2}{6},\qquad \Sigma_j(M_k)=\Sigma_{\lceil j/k\rceil}([z-w]),\quad j\ge1. $$ The proof exploits a residue-class d...
For $k\geq1$, let $M_k=[(z-w)^k]\subset H^2(\mathbb D^2)$. We first determine the banded Toeplitz matrices associated with the homogeneous components of $M_k$, together with explicit formulas for their determinants and the relevant algebraic cofactors. These formulas lead to a complete description of the spectrum of th...
Yin Liu, Yu-Feng Lu, Chao Zu· 1 citation
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