15 problems

Standard-circulant first appearance value conjecture. For $n \geq 2$,

Standard-circulant first appearance degree conjecture. For $n \geq 2$,

Let $R$ be a commutative finite chain ring (CFCR) of nilpotency index $e$, let $n$ be a positive integer, and suppose that the maximal ideal of $R$ is generated by $\gamma$. Write…

Let $R$ be a commutative finite chain ring (CFCR) of nilpotency index $e$, and let $n$ be a positive integer. Let $C_n(R)$ denote the ring of $n\times n$ circulant matrices over…

Let $n>4$, let $A$ be an $n\times n$ circulant matrix with entries in $\{-1,1\}$, and let $\|\cdot\|$ denote the Euclidean norm on $\mathbb R^n$. Quantitative Ryser conjecture. The…

Let $\mathcal{C}_d$ denote the set of circulant matrices, $\mathcal{U}_d$ the set of unistochastic matrices, and $\mathcal{C}_d^2$ the set of doubly circulant unistochastic matrice…

Let $p$ be a prime, let $G=SL_2(\mathbb{F}_p)$, and let $f:G\rightarrow\{0,1\}$ be chosen uniformly at random. Write $M_G(f)$ for the corresponding $G$-circulant matrix. Rigidity c…

Let $n$ be a positive integer. A Hadamard matrix of order $2n+2$ with two circulant cores is a matrix whose two core blocks $A$ and $B$ are circulant matrices of order $n$ and sati…

Let $p$ be a positive integer. A Hadamard matrix with one circulant core of order $p+1$ has block form $\left(\begin{smallmatrix}1&e\e^{t}&X_C\end{smallmatrix}\right)$, where…

One-circulant-core order claim. These are the only possible orders for a Hadamard matrix with one circulant core.

Let $C_n^{\operatorname{circ}}(\infty)$ denote the set of circulant complex Hadamard matrices of order $n$, with no fixed bound on the orders of their root-of-unity entries, and le…

For $N=4$, decompose the functional into components $\Phi=\Phi_0+\Phi_1+\Phi_2+\Phi_3$, where the $\Phi_i$ are the components defined in the preceding formulas. Parity conjecture f…

Let $N=4n$, and let … be minimized over vectors $q\in\mathbb T^N$ satisfying $\bar q_i=q_{-i}$. In the parametrization described immediately before the conjecture, write the corres…

Let $C_n^k$ be a circulant matrix, let $W\subset\mathbb Z_n$ define a relevant circulant minor isomorphic to $C_{n'}^{k'}$, and let $Q(C_n^k)$ denote the associated set covering po…

Let $C_m^d$ be the circulant associated with the degree-$d$ B-spline collocation matrix, with Toeplitz symbol coefficients $t_0^d,\ldots,t_r^d$, and let $\lambda_\mu(C_m^d)$ denote…