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| A001174
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Number of oriented graphs (i.e., digraphs with no bidirected edges) on n unlabeled nodes. Also number of complete digraphs on n unlabeled nodes. Number of antisymmetric relations (i.e., oriented graphs with loops) on n unlabeled nodes is A083670.
(history;
published version)
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#54 by Michael De Vlieger at Mon Jul 15 10:18:10 EDT 2024
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#53 by Stefano Spezia at Mon Jul 15 09:50:13 EDT 2024
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#52 by Chai Wah Wu at Mon Jul 15 09:36:43 EDT 2024
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#51 by Chai Wah Wu at Mon Jul 15 09:36:37 EDT 2024
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| PROG
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(Python)
from itertools import combinations
from math import prod, gcd, factorial
from fractions import Fraction
from sympy.utilities.iterables import partitions
def A001174(n): return int(sum(Fraction(3**(sum(p[r]*p[s]*gcd(r, s) for r, s in combinations(p.keys(), 2))+sum((q-1>>1)*r+(q*r*(r-1)>>1) for q, r in p.items())), prod(q**r*factorial(r) for q, r in p.items())) for p in partitions(n))) # Chai Wah Wu, Jul 15 2024
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| STATUS
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approved
editing
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#50 by Susanna Cuyler at Fri Oct 22 11:35:10 EDT 2021
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#49 by Michel Marcus at Thu Oct 21 23:57:36 EDT 2021
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#48 by Michel Marcus at Thu Oct 21 23:57:32 EDT 2021
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| LINKS
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T. R. Hoffman, and J. P. Solazzo, <a href="http://arxiv.org/abs/1408.0334">Complex Two-Graphs via Equiangular Tight Frames</a>, arXiv preprint arXiv:1408.0334 [math.CO], 2014-2017.
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| STATUS
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proposed
editing
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#47 by Michael De Vlieger at Thu Oct 21 18:11:07 EDT 2021
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#46 by Michael De Vlieger at Thu Oct 21 18:11:05 EDT 2021
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| LINKS
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Musa Demirci, Ugur Ana, and Ismail Naci Cangul, <a href="https://doi.org/10.1007/978-981-16-1402-6">Properties of Characteristic Polynomials of Oriented Graphs</a>, Proc. Int'l Conf. Adv. Math. Comp. (ICAMC 2020) Springer, see p. 60.
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approved
editing
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#45 by Bruno Berselli at Fri Jul 06 03:01:58 EDT 2018
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