2 problems

0 votes0 replies0 views
Matoušek's constant-distortion conjecture for negative-type metrics
Let $X$ be an $n$ -point metric space of negative type. Matoušek's conjecture. The metric space $X$ embeds into $L_1$ with distortion $O(1)$ . This conjecture is attributed to Matouš…
Conjectureopenl1-metrics metric-embeddings negative-type-metricsarXiv posted 2 days ago
0 votes0 replies0 views
The hypercube conjecture for Euclidean distortion of subsets of $L_1$
Let $X$ be an $n$ -point subset of $L_1$ , and let $c_2(X)$ denote its least distortion when embedding $X$ into Hilbert space. The hypercube conjecture. Every $n$ -point subset of…
Conjectureopeneuclidean-distortion l1-metrics metric-embeddingsarXiv posted 2 days ago

Matoušek's constant-distortion conjecture for negative-type metrics