A059083 -id:A059083 - cp's OEIS frontend

A059079 Number of n-element T_0-antichains on a labeled set.

2, 5, 19, 16654, 2369110564675, 5960531437586238714806902334250676, 479047836152505670895481840783987408043359908583921478726185296900312296071642855730299

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Dec 23 2000

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.

			a(0) = (1/0!)*[1!*e] = 2; a(1) = (1/1!)*[2!*e] = 5; a(2) = (1/2!)*([4!*e] - 2*[3!*e] + [2!*e]) = 19; a(3) = (1/3!)*([8!*e] - 6*[6!*e] + 6*[5!*e] + 3*[4!*e] - 6*[3!*e] + 2*[2!*e]) = 16654, where [n!*e]=floor(n!*exp(1)).

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.

Vladeta Jovovic, Illustration

Cf. A059080-A059083, A059048-A059052, A000522.

A059080 Triangle A(n,m) of numbers of n-element T_0-antichains on a labeled m-set, m=0,...,2^n.

Original entry on oeis.org

1, 1, 1, 2, 2, 0, 0, 1, 6, 12, 0, 0, 0, 2, 52, 520, 2640, 6720, 6720, 0, 0, 0, 0, 25, 1770, 53940, 1012620, 13487040, 136745280, 1094688000, 7025356800, 36084787200, 145297152000, 435891456000, 871782912000, 871782912000

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Dec 29 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. Row sums give A059079. Column sums give A059083.

			[1, 1], [1, 2, 2], [0, 0, 1, 6, 12], [0, 0, 0, 2, 52, 520, 2640, 6720, 6720], ...; there are 2 3-element T_0-antichains on a 3-set: {{1}, {2}, {3}}, {{1, 2}, {1, 3}, {2, 3}}.

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 T_0-antichains on a labeled 4-set
V. Jovovic, Formula for the number of m-element T_0-antichains on a labeled n-set

Cf. A059079, A059081-A059083, A059048-A059052.

A059081 Number of 5-element T_0-antichains on a labeled n-set, n=0,..,32.

Original entry on oeis.org

0, 0, 0, 0, 6, 2086, 273072, 19371912, 940055760, 35289051840, 1099827892800, 29723466326400, 716351882400000, 15683016533184000, 315722887044364800, 5890186860509952000, 102288867798813696000, 1656523525703574528000

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.

G. C. Greubel, Table of n, a(n) for n = 0..32
Vladeta Jovovic, Formula for the number of m-element T_0-antichains on a labeled n-set

Cf. A059079, A059080, A059082, A059083, A059048-A059052.

P[x_, n_] := (-1)^n*Pochhammer[-x, n]; Table[(1/5!)*(P[32, n] - 20*P[24, n] + 60*P[20, n] + 20*P[18, n] + 10*P[17, n] - 110*P[16, n] - 120*P[15, n] + 150*P[14, n] + 120*P[13, n] - 240*P[12, n] + 20*P[11, n] + 240*P[10, n] + 40*P[9, n] - 205*P[8, n] + 60*P[7, n] - 210*P[6, n] + 210*P[5, n] + 50*P[4, n] - 100*P[3, n] + 24*P[2, n]), {n, 0, 32}] (* G. C. Greubel, Oct 07 2017 *)

a(n) = (1/5!)*([32]_n - 20*[24]_n + 60*[20]_n + 20*[18]_n + 10*[17]_n - 110*[16]_n - 120*[15]_n + 150*[14]_n + 120*[13]_n - 240*[12]_n + 20*[11]_n + 240*[10]_n + 40*[9]_n - 205*[8]_n + 60*[7]_n - 210*[6]_n + 210*[5]_n + 50*[4]_n - 100*[3]_n + 24*[2]_n), where [k]_n := k*(k - 1)*...*(k - n + 1), [k]_0 = 1.

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

A088888 Number of intersecting T_0-hypergraphs on a labeled n-set.

Original entry on oeis.org

2, 4, 26, 1190, 1302204, 912799349556, 291201248247281713961832

Offset: 1

Goran Kilibarda, Vladeta Jovovic, Nov 28 2003

Intersecting hypergraph is intersecting T_0-hypergraph if for every two distinct nodes there exists a hyperedge containing one but not the other node.

Cf. A051185, A059083.

A088895 Number of intersecting T_0-antichains on a labeled n-set.

Original entry on oeis.org

1, 2, 2, 4, 41, 2104, 1387915, 229780525655

Offset: 0

Goran Kilibarda, Vladeta Jovovic, Nov 28 2003

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

Cf. A001206, A051185, A059083.

cp's OEIS Frontend

A059079 Number of n-element T_0-antichains on a labeled set.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

A059080 Triangle A(n,m) of numbers of n-element T_0-antichains on a labeled m-set, m=0,...,2^n.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

A059081 Number of 5-element T_0-antichains on a labeled n-set, n=0,..,32.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

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

A088888 Number of intersecting T_0-hypergraphs on a labeled n-set.

Views

Author

Keywords

Comments

Crossrefs

A088895 Number of intersecting T_0-antichains on a labeled n-set.

Views

Author

Keywords

Comments

Crossrefs