cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A382018 Number of orbits under the action of the permutation group S(n) on the nonsingular n X n matrices over GF(2).

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%I A382018 #18 Aug 15 2025 15:55:04
%S A382018 1,1,4,33,908,85411,28227922,32597166327
%N A382018 Number of orbits under the action of the permutation group S(n) on the nonsingular n X n matrices over GF(2).
%C A382018 The action is defined by f.M(i,j)=M(f(i),f(j)).
%C A382018 Equivalently, the number of digraphs on n unlabeled nodes with loops allowed but no more than one arc with the same start and end node with adjacency matrices invertible over GF(2).
%H A382018 Jens Emil Christensen, Søren Fuglede Jørgensen, Andreas Pavlogiannis, and Jaco van de Pol, <a href="https://doi.org/10.1007/978-3-031-97063-4_6">On Exact Sizes of Minimal CNOT Circuits</a>, RC 2025, LNCS, vol 15716, pp. 71-88; <a href="https://arxiv.org/abs/2503.01467">arXiv:2503.01467</a> [quant-ph], 2025, Table 1.
%e A382018 For n = 2, representatives of the four different orbits are [[1, 0], [0, 1]], [[1, 1], [0, 1]], [[0, 1], [1, 1]], and [[0, 1], [1, 0]].
%Y A382018 Cf. A000595, A002884, A224879.
%K A382018 nonn,hard,more
%O A382018 0,3
%A A382018 _Søren Fuglede Jørgensen_, Mar 12 2025