Cosmas Kravaris

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20242026

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math.MG2025

$L_{1}$ and $L_{2}$ embeddings of the symmetric group

Cosmas Kravaris

We show that the Cayley graph of the symmetric group $S y m_{n}$ generated by the cycle $(123... n)$ and the transposition $(12)$ embeds into $L_{1}$ with bi-Lipschitz distortion $O (1)$ .…

math.MG2024

Lower bounds for the universal TSP on the plane

Cosmas Kravaris

We show a lower bound for the universal traveling salesman heuristic on the plane: for any linear order on the unit square $[0, 1]^{2}$ , there are finite subsets $S \subset [0, 1]^{2}$ o…

L1​ and L2​ embeddings of the symmetric group

Lower bounds for the universal TSP on the plane

$L_{1}$ and $L_{2}$ embeddings of the symmetric group