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Added a link to the book of Deza and Laurent in RG
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Taras Banakh
Taras Banakh
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In "Geometry of cuts and metrics""Geometry of cuts and metrics" by Deza and Laurent, your inequality is called pure inequality of negative type.

In Section 6.1.1, it is stated that pure inequalities of negative type imply all inequalities of negative type.

In Theorem 6.2.2 they formulate Schoenberg's criterion: a metric space admits an isometric embedding into a Hilbert space if and only it the square of the metric satisfies all the inequalities of negative type.

In "Geometry of cuts and metrics" by Deza and Laurent, your inequality is called pure inequality of negative type.

In Section 6.1.1, it is stated that pure inequalities of negative type imply all inequalities of negative type.

In Theorem 6.2.2 they formulate Schoenberg's criterion: a metric space admits an isometric embedding into a Hilbert space if and only it the square of the metric satisfies all the inequalities of negative type.

In "Geometry of cuts and metrics" by Deza and Laurent, your inequality is called pure inequality of negative type.

In Section 6.1.1, it is stated that pure inequalities of negative type imply all inequalities of negative type.

In Theorem 6.2.2 they formulate Schoenberg's criterion: a metric space admits an isometric embedding into a Hilbert space if and only it the square of the metric satisfies all the inequalities of negative type.

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Anton Petrunin
Anton Petrunin
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In "Geometry of cuts and metrics" by Deza and Laurent, your inequality is called pure inequality of negative type.

In Section 6.1.1, it is stated that pure inequalities of negative type imply all inequalities of negative type.

In Theorem 6.2.2 they formulate Schoenberg's criterion: a metric space admits an isometric embedding into a Hilbert space if and only it the square of the metric satisfies all the inequalities of negative type.