S. Kominers

collaborators

25 papers

math.GM2026

A proper Euler magic matrix of order $5$

Scott Duke Kominers

An Euler magic matrix is an integer matrix $M$ with $M M^{t} = I^^{3} I$ whose squared entries sum to $I^^{3}$ along both main diagonals; it is proper if its squared entries are pairwise disti…

math.NT2026

Long Intervals Without Distinct Multiples of the First $n$ Positive Integers

Scott Duke Kominers

For positive integers $n$ and $m$ , let $f (n, m)$ be the least integer $h \geq 0$ such that $(m, m + h]$ contains distinct integers $a_{1}, \dots, a_{n}$ satisfying $i ∣ a_{i}$ for $1\le i\le n…

math.HO2026

Palindromes on the $I ¨ $ -circle: A note for Palindrome Tau Day, 6/28/26

Scott Duke Kominers

An integer palindrome is a self-reciprocal polynomial evaluated at its base, so its roots are symmetric about the unit circle -- where the coordinate is angle, in turns of $I ¨ $ . Re…

math.NT2026

For which real quadratic fields is Kim's octonary form universal?

Scott Duke Kominers

Let $K = Q (D)$ with $D > 1$ squarefree, and let $ε_{+}$ be the totally positive fundamental unit of $O_{K}$ . B. M. Kim proved in 2000 that the octonary…

math.MG2026

A reduced planar body with area greater than $I ¨ I^^{2} /4$

Scott Duke Kominers

We construct a reduced planar convex body $R$ with thickness $I^ (R) = 1$ and \[\operatorname{area}(R)=0.786215\ldots>0.785398\ldots=\fracÏ{4}.\] Thus $R$ is a counterexample to Lass…

math.CO2026

An eigenvalue proof of HegedÃ¼s's bound for codes with a single Hamming distance

Scott Duke Kominers

We give a short, self-contained linear-algebra proof of a bound of HegedÃ¼s [Australasian Journal of Combinatorics, 2026; arXiv:2409.07877]: if all pairwise Hamming distances in a…

A proper Euler magic matrix of order 5

Long Intervals Without Distinct Multiples of the First n Positive Integers

Palindromes on the I¨-circle: A note for Palindrome Tau Day, 6/28/26

For which real quadratic fields is Kim's octonary form universal?

A reduced planar body with area greater than I¨I^2/4

An eigenvalue proof of HegedÃ¼s's bound for codes with a single Hamming distance

A proper Euler magic matrix of order $5$

Long Intervals Without Distinct Multiples of the First $n$ Positive Integers

Palindromes on the $I ¨ $ -circle: A note for Palindrome Tau Day, 6/28/26

A reduced planar body with area greater than $I ¨ I^^{2} /4$