The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A053043

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A053043

Number of facets of hypermetric correlation cone.
(history; published version)

#14 by Peter Luschny at Sun Jul 03 06:45:47 EDT 2022

STATUS

reviewed

approved

#13 by Joerg Arndt at Sun Jul 03 01:54:50 EDT 2022

STATUS

proposed

reviewed

#12 by Jon E. Schoenfield at Sat Jun 25 20:36:29 EDT 2022

STATUS

editing

proposed

Discussion

Sun Jun 26

03:32

Andrey Zabolotskiy: Yes, thanks.

#11 by Jon E. Schoenfield at Sat Jun 25 20:34:42 EDT 2022

COMMENTS

In Table 1 of Deza & Dutour Sikirić 2018 (also in Table 13.1 on p. 223 of "Generalizations Of of Finite Metrics And and Cuts"), the same initial terms are given for the number of facets of the hypermetric cone HYP_{n-1}, with the next term 298592. However, the hypermetric cone HYP and the hypermetric correlation cone HYCO apparently have different definitions. - Andrey Zabolotskiy, Jun 25 2022

REFERENCES

Elena Deza, Michel Deza and Mathieu Dutour Sikirić, Generalizations Of of Finite Metrics And and Cuts, World Scientific, 2016.

STATUS

proposed

editing

Discussion

Sat Jun 25

20:36

Jon E. Schoenfield: Minor changes to capitalization okay? 
 based on what I found at https://www.worldscientific.com/worldscibooks/10.1142/9906

#10 by Andrey Zabolotskiy at Sat Jun 25 06:37:30 EDT 2022

STATUS

editing

proposed

#9 by Andrey Zabolotskiy at Sat Jun 25 06:37:22 EDT 2022

CROSSREFS

Cf. A235459.

STATUS

proposed

editing

#8 by Andrey Zabolotskiy at Sat Jun 25 06:15:10 EDT 2022

STATUS

editing

proposed

#7 by Andrey Zabolotskiy at Sat Jun 25 05:47:19 EDT 2022

COMMENTS

In Table 1 of Deza & Dutour Sikirić 2018 (also in Table 13.1 on p. 223 of "Generalizations Of Finite Metrics And Cuts"), the same initial terms are given for the number of facets of the hypermetric cone HYP_{n-1}, with the next term 298592. However, the hypermetric cone HYP and the hypermetric correlation cone HYCO apparently have different definitions. - Andrey Zabolotskiy, Jun 25 2022

REFERENCES

Elena Deza, Michel Deza and Mathieu Dutour Sikirić, Generalizations Of Finite Metrics And Cuts, World Scientific, 2016. See Table 13.1 on p. 223.

Discussion

Sat Jun 25

05:59

Andrey Zabolotskiy: In fact, the hypermetric cone HYP_n is mentioned much more often in the literature than the hypermetric correlation cone HYCO_n, so perhaps it makes sense to make the primary definition of this sequence based on HYP rather than HYCO.

06:11

Andrey Zabolotskiy: On the other hand, the wording of Deza & Grishukhin, the way they reference papers about HYP, suggests that HYCO and HYP is actually the same of very closely related things. But why the difference in the offset than?.. OK, HYCO_n is a cone in the space of real symmetrix nXn matrices, which is n*(n+1)/2-dimensional, while HYP_n [according to Deza & Dutour Sikirić 2018] is a cone in the space of real symmetric matrices with zeros in the diagonal, which is (n-1)*n/2-dimensional, OK, this explains the difference in the offset. The relation between them is not obvious from the first sight though.

06:15

Andrey Zabolotskiy: Whatever.

#6 by Andrey Zabolotskiy at Sat Jun 25 05:42:40 EDT 2022

DATA

3, 12, 40, 210, 3773, 298592

EXTENSIONS

a(7) from "Generalizations Of Finite Metrics And Cuts" added by Andrey Zabolotskiy, Jun 24 2022

#5 by Andrey Zabolotskiy at Fri Jun 24 16:09:52 EDT 2022

LINKS

Michel Deza and Mathieu Dutour Sikirić, <a href="https://doi.org/10.1016/j.jsc.2016.01.009">The hypermetric cone and polytope on eight vertices and some generalizations</a>, Journal of Symbolic Computation, 88 (2018), 67-84.