Main metric invariants of finite metric spaces. II (Q308877)

Let \({\mathcal K}\) denote the collection of all finite metric space with the same cardinality \(N> 1\). The following is the main result in this paper: Theorem. Let the numbers \((K,m,T,k)\) be given as \(4\leq K\leq N\), \(1\leq m\leq K(K-1)/2\), \(1\leq T\leq [N/2]\), \(1\leq k\leq T(N-T)\). Then, the functions \(\mathrm{mild}_{mK}\), \(\mathrm{mald}_{mK}\), \(\mathrm{milc}_{kT}\), \(\mathrm{malc}_{kT}\) are main metric invariants. This result may be viewed as a continuation of the related ones in the author's paper [Russ. Math. 59, No. 5, 38--40 (2015; Zbl 1321.54054); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2015, No. 5, 45--48 (2015)].