A185178 Number of distinct values of the permanent of an n X n (0,1)-matrix with exactly three 1's in each row and each column.

1, 1, 2, 4, 8, 18, 32, 61, 109

Offset: 3

Author

Vladimir Shevelev, Feb 19 2011

Keywords

• nonn
• hard
• more

Comments

The values a(n) are unknown for n>=9.

a(12) >= 170, a(13) >= 276, a(14) >= 438, a(15) >= 547. - Robert P. P. McKone, Jul 14 2025

References

• V. I. Bolshakov, On spectrum of permanent on Lambda_n^k, Proc. of Seminar on Discrete Math. and Appl., Moscow State Univ. (1986), 65-73 (in Russian).

Links

• Robert P. P. McKone, One example matrix for each known permanent for a(3)..a(15), with a(11)..a(15) being incomplete
• Robert P. P. McKone, Complete frequence counts for each permanent for a(3)..a(11)
• Robert P. P. McKone, Robert P. P. McKone, C++ code for enumerating and counting each permanent's frequency for a(n)
• V. S. Shevelev, Some problems of the theory of enumerating the permutations with restricted position, Journal of Soviet Mathematics, 61 (4) (1992) 2272-2317 (see pp. 2307-2309).

Crossrefs

Cf. A185179 (values of the permanent), A176211, A176212.

Cf. A001501 (number of n X n (0,1)-matrix with exactly three 1's in each row and each column).

Extensions

a(9)-a(11) from Robert P. P. McKone, Jul 22 2025