15 problems

Anand–Dumir–Gupta conjecture. The function $H_n(r)$ is a polynomial in $r$ of degree $(n-1)^2$ with certain additional properties.

Let $N=nt$, where $n$ is the dimension and $t$ is the common line sum of an $n\times n$ magic square. The paper gives an approximation algorithm for $|\Sigma(n,t)|$ with running ti…

Let $P$ be the Birkhoff polytope, whose points are the real doubly stochastic $n\times n$ matrices, and let $E(P)$ be the affine monoid encoding the magic squares. Question (ii) as…

Let $([d],\mathcal{L})$ be a covering clutter, let $s$ be its magic subspace, and let a magic permutation be a permutation of $[d]$ realizable by a positive point in $s$. For a per…

Let $n$ be a positive integer, let $H_n(r)$ denote the number of $n\times n$ magic squares with line sums equal to $r$, and write … where $d=n^2-3n+2$ and $h_0=1$, $h_i=h_{d-i}$ fo…

Let $M_n$, $S_n$, and $P_n$ denote the counting functions for the magic squares considered in the paper, with parameter $n$. Nonpolynomiality conjecture. The functions $M_n$, $S_n$…

Let $n$ be a positive integer, let $[1,n]=\{1,\ldots,n\}$, and let $a_{\min}$ and $a_{\max}$ define the allowed integer range for the entries of an $n\times n$ magic square. The co…

For an integer $n$, an $n \times n$ magic square of squares is a magic square whose entries are squares. Várilly-Alvarado's conjecture. There is a positive integer $n_0(2)$ such th…

Conjecture 9.4. The largest Parker ring of the form $\mathbb{Z}/n\mathbb{Z}$ is

Conjecture 9.3. Among Parker rings of the form $\mathbb{Z}/n\mathbb{Z}$ with $n$ odd, the largest is

Conjecture 9.2. If $\mathbb{Z}/n\mathbb{Z}$ is a record modulus, then

Conjecture 7.1. The only Parker fields of prime order are the fields listed above.

Let $(p,q,r)$-boards be the three-dimensional boards considered in the paper, and let a board be Cartesian bi-magic when it admits a Cartesian bi-magic labeling. Cartesian bi-magic…

Let $k$ be the parameter in the construction $(M_n)$ of the higher-order-$k^2$ pandiagonal super-sudoku squares, and call the resulting panmagic square natural when it has no dupli…

A Knut Vik sudoku square (also called a Latin pandiagonal sudoku square) is a sudoku square satisfying the Knut Vik, or Latin pandiagonal, condition. Ollerenshaw's conjecture. Ther…