A059049 -id:A059049 - cp's OEIS frontend

A059052 Number of n-element unlabeled ordered T_0-antichains; T_1-hypergraphs (with empty hyperedge but without multiple hyperedges) on n labeled nodes.

2, 4, 4, 72, 38040, 4020463392, 18438434825136728352, 340282363593610211921722192165556850240, 115792089237316195072053288318104625954343609704705784618785209431974668731584

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Dec 19 2000

nonn

An antichain on a set is a T_0-antichain if for every two distinct points of the set there exists a member of the antichain containing one but not the other point. T_1-hypergraph is a hypergraph which for every ordered pair (u,v) of distinct nodes has a hyperedge containing u but not v.

			a(3) = 2 + 13 + 26 + 22 + 8 + 1. a(6) = 2^64 - 30*2^48 + 120*2^40 + 60*2^36 + 60*2^34 - 12*2^33 - 345*2^32 - 720*2^30 + 810*2^28 + 120*2^27 + 480*2^26 + 360*2^25 - 480*2^24 - 720*2^23 - 240*2^22 - 540*2^21 + 1380*2^20 + 750*2^19 + 60*2^18 - 210*2^17 - 1535*2^16 - 1820*2^15 + 2250*2^14 + 1800*2^13 - 2820*2^12 + 300*2^11 + 2040*2^10 + 340*2^9 - 1815*2^8 + 510*2^7 - 1350*2^6 + 1350*2^5 + 274*2^4 - 548*2^3 + 120*2^2.

V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, in Russian, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, English translation, in Discrete Mathematics and Applications, 9, (1999), no. 6.

Cf. A059048, A059049, A059050, A059051, A326960.

a(n) = Sum_{m=0..2^n} A(n, m), where A(n, m) is number of n-element ordered T_0-antichains on an unlabeled m-set. Cf. A059048.

a(n) = row sums of A059048.

A059048 Triangle A(n,m) of numbers of n-element ordered T_0-antichains on an unlabeled m-set or numbers of T_1-hypergraphs on n labeled nodes with m (not necessarily empty) distinct hyperedges (m=0,1,...,2^n).

Original entry on oeis.org

1, 1, 1, 2, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 13, 26, 22, 8, 1, 0, 0, 0, 0, 25, 354, 1798, 4822, 8028, 9044, 7240, 4224, 1808, 560, 120, 16, 1, 0, 0, 0, 0, 30, 2086, 45512, 461236, 2797785, 11669660, 36369970, 89356260, 179461250, 302225100, 43458923, 0

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Dec 19 2000

nonn

			[1, 1], [1, 2, 1], [0, 0, 1, 2, 1], [0, 0, 0, 2, 13, 26, 22, 8, 1], .... There are 72 3-element unlabeled ordered T_0-antichains: 2 on 3-set, 13 on 4-set, 26 on 5-set, 22 on 6-set, 8 on 7-set and 1 on 8-set.

V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

V. Jovovic, 3-element unlabeled ordered T_0-antichains"
V. Jovovic, Number A(m,n) of m-element ordered T_0-antichains on an unlabeled n-set

Cf. A059049-A059052.

A059050 Number of 7-element ordered T_0-antichains on an unlabeled n-set; T_1-hypergraphs on 7 labeled nodes with n (not necessarily empty) distinct hyperedges (n=0,1,...,128).

Original entry on oeis.org

0, 0, 0, 0, 0, 20580, 9106440, 1058272828, 56671435220, 1819138009252, 40526220292026, 685404291322800, 9333711208757096, 106588763704012184, 1051025434717631806, 9144977489478933912, 71381946761468630363

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Dec 19 2000

V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

Sean A. Irvine, Table of n, a(n) for n = 0..128

Cf. A059048, A059049, A059051, A059052.

a(n)=C(128, n) - 42*C(96, n) + 210*C(80, n) + 140*C(72, n) + 210*C(68, n) - 84*C(66, n) + 14 *C(65, n) - 819*C(64, n) - 2520*C(60, n) + 2730*C(56, n) + 840*C(54, n) + 840*C(52, n) - 420*C(51, n) + 2940*C(50, n) + 630*C(48, n) - 5040*C(46, n) + 840*C(45, n) - 1260*C(44, n) + 1680*C(43, n) - 9660*C(42, n) + 1260*C(41, n) + 3360*C(40, n) - 7560*C(39, n) + 11130*C(38, n) + 5880*C(37, n) + 9240*C(36, n) + 2982*C(35, n) - 6300*C(34, n) - 8652 *C(33, n) - 9905*C(32, n) - 8400*C(31, n) - 8540*C(30, n) + 13860*C(29, n) + 14490 *C( 28, n) - 5040*C(27, n) + 10500*C(26, n) + 10080*C(25, n) - 8120*C(24, n) - 15050*C(23, n) - 5040*C(22, n) - 11340*C(21, n) + 20580*C(20, n) + 15750*C(19, n) - 1540*C(18, n) - 5810*C(17, n) - 16485*C(16, n) - 21420*C(15, n) + 26250*C(14, n) + 21000*C(13, n) - 29820*C(12, n) + 3500*C(11, n) + 17640*C(10, n) + 2940*C(9, n) - 16016*C(8, n) + 4410*C(7, n) - 9744*C(6, n) + 9744*C(5, n) + 1764*C(4, n) - 3528*C(3, n) + 720*C(2, n).

A059082 Number of 6-element T_0-antichains on a labeled n-set, n = 0, ..., 64.

Original entry on oeis.org

0, 0, 0, 0, 1, 1370, 738842, 176796382, 26021566536, 2807549333568, 245222809302240, 18418417704308160, 1236761946163054080, 76210520306627266560, 4388527139331858082560, 239214759548062858560000, 12457699161320493400320000, 623967599346727576292352000

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Jan 06 2001

An antichain on a set is a T_0-antichain if for every two distinct points of the set there exists a member of the antichain containing one but not the other point.

V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

Alois P. Heinz, Table of n, a(n) for n = 0..64
V. Jovovic, Formula for the number of m-element T_0-antichains on a labeled n-set

Cf. A059079, A059080, A059081, A059083, A059048, A059049, A059050, A059051, A059052.

f:=proc(k,n) if k+1<=n then RETURN(0) else RETURN(k!/(k - n)!) fi: end;a:=n->(1/6!)*(f(64,n) - 30*f(48,n) + 120*f(40,n) + 60*f(36,n) + 60*f(34,n)- 12*f(33,n) - 345*f(32,n) - 720*f(30,n) + 810*f(28,n) + 120*f(27,n) + 480*f(26,n) + 360*f(25,n) - 480*f(24,n) - 720*f(23,n) - 240*f(22,n) - 540*f(21,n) + 1380*f(20,n) + 750*f(19,n) + 60*f(18,n) - 210*f(17,n) - 1535*f(16,n) - 1820*f(15,n) + 2250*f(14,n) + 1800*f(13,n) - 2820*f(12,n) + 300*f(11,n) + 2040*f(10,n) + 340*f(9,n) - 1815*f(8,n) + 510*f(7,n) - 1350*f(6,n) + 1350*f(5,n) + 274*f(4,n) - 548*f(3,n) + 120*f(2,n));seq(a(n),n=0..20); # Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005

a(n) = (1/6!)*([64]_n - 30*[48]_n + 120*[40]_n + 60*[36]_n + 60*[34]_n - 12*[33]_n - 345*[32]_n - 720*[30]_n + 810*[28]_n + 120*[27]_n + 480*[26]_n + 360*[25]_n - 480*[24]_n - 720*[23]_n - 240*[22]_n - 540*[21]_n + 1380*[20]_n + 750*[19]_n + 60*[18]_n - 210*[17]_n - 1535*[16]_n - 1820*[15]_n + 2250*[14]_n + 1800*[13]_n - 2820*[12]_n + 300*[11]_n + 2040*[10]_n + 340*[9]_n - 1815*[8]_n + 510*[7]_n - 1350*[6]_n + 1350*[5]_n + 274*[4]_n - 548*[3]_n + 120*[2]_n), where [k]_n := k*(k - 1)*...*(k - n + 1), [k]_0 = 1.

More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005

cp's OEIS Frontend

A059052 Number of n-element unlabeled ordered T_0-antichains; T_1-hypergraphs (with empty hyperedge but without multiple hyperedges) on n labeled nodes.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Formula

A059048 Triangle A(n,m) of numbers of n-element ordered T_0-antichains on an unlabeled m-set or numbers of T_1-hypergraphs on n labeled nodes with m (not necessarily empty) distinct hyperedges (m=0,1,...,2^n).

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

A059050 Number of 7-element ordered T_0-antichains on an unlabeled n-set; T_1-hypergraphs on 7 labeled nodes with n (not necessarily empty) distinct hyperedges (n=0,1,...,128).

Views

Author

Keywords

Comments

References

Links

Crossrefs

Formula

A059082 Number of 6-element T_0-antichains on a labeled n-set, n = 0, ..., 64.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Maple

Formula

Extensions