Tootfinder

A New Method of Constructing Hadamard Matrices, Circulant Hadamard Matrices, CZCS, GCS, CCC, and CZCSS
Piyush Priyanshu, Sudhan Majhi, Subhabrata Paul
https://arxiv.org/abs/2510.12315

A New Method of Constructing Hadamard Matrices, Circulant Hadamard Matrices, CZCS, GCS, CCC, and CZCSS
A Hadamard matrix $H$ is a square matrix of order $n$ with entries $\pm 1$, such that $HH^\top=nI_{n}$, where $I_n$ is an identity matrix of order $n$. A circulant Hadamard matrix $H$ is a Hadamard matrix that has rows of entries in cyclic order. There exist only $8$ circulant Hadamard matrices of order 4, and here, we provide a novel construction of all such $8$ circulant Hadamard matrices using a linear operator and generalized Boolean function (GBF). The constructed circulant Hadamard matric…

An update on the existence of integer Heffter arrays
Fiorenza Morini, Marco Antonio Pellegrini
https://arxiv.org/abs/2510.08302 https://arxiv.org/pdf/2510.…

An update on the existence of integer Heffter arrays
An integer Heffter array $H(m,n;s;k)$ is an $m\times n$ partially filled array whose entries are the elements of a subset $Ω\subset \mathbb{Z}$ such that $\{Ω,-Ω\}$ is a partition of the set $\{1,2,\ldots,2nk\}$ and such that the following conditions are satisfied: each row contains $s$ filled cells, each column contains $k$ filled cells, the elements in every row and column add up to $0$. It was conjectured by Dan Archdeacon that an integer $\H(m,n;s;k)$ exists if and only if $ms=nk$, $3\le…

Counting 2x2 integer matrices with a given determinant
Jonathan Chapman, Akshat Mudgal
https://arxiv.org/abs/2509.20259 https://arxiv.org/pdf/2509.20259

Counting 2x2 integer matrices with a given determinant
Given positive integers $h, N$ satisfying $1 \leqslant h \leqslant 2N^2$, we define $T(h,N)$ to be the number of $2\times 2$ integer matrices with determinant equal to $h$ whose entries lie in $[-N,N]$. Our first result states that for any $\varepsilon >0$, one has \[ T(h,N) = \frac{16}{ζ(2)} N^2 \bigg( \sum_{d |h} \frac{1}{d} \bigg) + O_{\varepsilon}(N^{\varepsilon} (N+ h)).\] This quantitatively improves upon recent work of Afifurrahman and Ganguly--Guria. We further show that when $N^{…

RE: https://mastodon.social/@cheeaun/115415146417702654
After looking at this, got curious to know the limits in most servers.
So I did a little data analysis. Servers list from @…

Linear Regression under Missing or Corrupted Coordinates
Ilias Diakonikolas, Jelena Diakonikolas, Daniel M. Kane, Jasper C. H. Lee, Thanasis Pittas
https://arxiv.org/abs/2509.19242