Noah Kravitz

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20182026

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math.CO2022

Cats in cubes

Noga Alon, Noah Kravitz

Answering a recent question of Patchell and Spiro, we show that when a $d$ -dimensional cube of side length $n$ is filled with letters, the word $CAT$ can appear contiguous…

math.CO2022

Foot-Sorting for Socks

Colin Defant, Noah Kravitz

If your socks come out of the laundry all mixed up, how should you sort them? We introduce and study a novel foot-sorting algorithm that uses feet to attempt to sort a sock orderin…

math.CO2022

Logarithmically larger deletion codes of all distances

Noga Alon, Gabriela Bourla, Ben Graham +2

The deletion distance between two binary words $u, v \in {0, 1}^{n}$ is the smallest $k$ such that $u$ and $v$ share a common subsequence of length $n - k$ . A set $C$ of binary words o…

math.CO2022

Extensions of Hitomezashi Patterns

Colin Defant, Noah Kravitz, Bridget Eileen Tenner

Hitomezashi, a form of traditional Japanese embroidery, gives rise to intricate arrangements of axis-parallel unit-length stitches in the plane. Pete studied these patterns in the…

math.CO2022

Counting Dope Matrices

Noga Alon, Noah Kravitz, Kevin O'Bryant

For a polynomial $P$ of degree $n$ and an $m$ -tuple $Λ = (λ_{1}, \dots, λ_{m})$ of distinct complex numbers, the dope matrix of $P$ with respect to $Λ$ is $D_P(Λ)=(δ_{ij})_{i\in [1,m],j\in…

math.CO2022

Loops and Regions in Hitomezashi Patterns

Colin Defant, Noah Kravitz

Hitomezashi patterns, which originate from traditional Japanese embroidery, are intricate arrangements of unit-length line segments called stitches. The stitches connect to form hi…