A000794 Permanent of the Desarguesian projective plane PG(2,n), or 0 if such plane does not exist. (Formerly M2143 N2248)

1, 2, 24, 3852, 18534400, 4598378639550, 0

Offset

0,2

References

H. J. Ryser, Combinatorial Mathematics. Mathematical Association of America, Carus Mathematical Monograph 14, 1963, p. 124.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..6.

Shamil Asgarli and Brian Freidin, On the proportion of transverse-free plane curves, arXiv:2009.13421 [math.AG], 2020.

Zeynelabidin Karakaş, Classification of Distinct Maximal Flag Codes of a Prescriped Type and Related Results, PhD Thesis, Middle East Technical University, 2023. See pages 40 and 43.

Georg Muntingh, Sage code for constructing the incidence matrix of the projective plane over a finite field of order n, and its permanent.

Georg Muntingh, Incidence matrix of a projective plane over a finite field of order 2, 3, 4, 5, 7, 8, and 9.

P. J. Nikolai, Permanents of incidence matrices, Math. Comp., 14 (1960), 262-266.

Example

From Georg Muntingh, Feb 03 2014: (Start)
The projective plane over a finite field of order 2 has 7 points and 7 lines, for instance meeting with the incidence matrix
    [1 0 0 1 1 0 0]
    [0 1 1 0 1 0 0]
    [1 0 1 0 0 1 0]
    [0 1 0 1 0 1 0]
    [0 0 1 1 0 0 1]
    [1 1 0 0 0 0 1]
    [0 0 0 0 1 1 1]
which has permanent 24.  (End)

Crossrefs

Sequence in context: A111430 A355561 A059332 * A242484 A159907 A088912

Adjacent sequences: A000791 A000792 A000793 * A000795 A000796 A000797

Keyword

nonn,more,changed

Author

N. J. A. Sloane

Extensions

a(5) from Georg Muntingh, Feb 03 2014

Offset corrected, definition clarified, and a(6)=0 added by Max Alekseyev, Nov 15 2025

Status

approved