The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A346179

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A346179

Number of nonisomorphic vertex-transitive tournaments of order 2n-1.
(history; published version)

#7 by N. J. A. Sloane at Fri Jul 09 22:20:58 EDT 2021

STATUS

proposed

approved

#6 by Alois P. Heinz at Fri Jul 09 13:07:20 EDT 2021

STATUS

editing

proposed

#5 by Alois P. Heinz at Fri Jul 09 13:07:05 EDT 2021

CROSSREFS

Cf. A060747.

#4 by Alois P. Heinz at Fri Jul 09 13:05:15 EDT 2021

NAME

Number of nonisomorphic vertex-transitive tournaments of order 2n-1.

STATUS

proposed

editing

#3 by Brendan McKay at Fri Jul 09 06:23:43 EDT 2021

STATUS

editing

proposed

Discussion

Fri Jul 09

07:17

Hugo Pfoertner: Is there any connection to A139292, which is a search hit for 21,25,27,...49? The occurrence of "noncyclic" there would at least be a funny coincidence.

07:20

Hugo Pfoertner: Sorry, A139292 should be A139392.

08:36

Jon E. Schoenfield: Name needs to end with a period.

08:52

Brendan McKay: The occurrence of non-circulant vertex-transitive tournaments relies on certain permutation groups appearing, which depends on the factorization of the degree. However, "relies" is a bit vague and I doubt if a strict connection has been proved. The group theory is deep and beyond me.

#2 by Brendan McKay at Fri Jul 09 06:22:53 EDT 2021

NAME

allocated for Brendan McKayNumber of nonisomorphic vertex-transitive tournaments of order 2n-1

DATA

1, 1, 1, 2, 3, 4, 6, 16, 16, 30, 110, 94, 214, 694, 586, 1096, 3280, 5472, 7286, 25206, 26216, 49940, 196624, 182362, 407856, 907116

OFFSET

1,4

COMMENTS

The circulant tournaments A049288 are included.

Up to 49 vertices, non-circulant vertex-transitive tournaments occur on 21, 25, 27, 39, 45 and 49 vertices.

LINKS

Brendan McKay, <a href="http://users.cecs.anu.edu.au/~bdm/data/digraphs.html">vertex-transitive tournaments</a>

CROSSREFS

If the automorphism group contains a full-length cycle, the tournament is circulant and is counted by A049288.

KEYWORD

allocated

nonn,hard,more

AUTHOR

Brendan McKay, Jul 09 2021

STATUS

approved

editing

#1 by Brendan McKay at Fri Jul 09 06:22:53 EDT 2021

NAME

allocated for Brendan McKay

KEYWORD

allocated

STATUS

approved