Wilf A. Wilson - cp's OEIS frontend

A290289 The number of maximal subsemigroups of the monoid of partial orientation-preserving and reversing injective mappings on the set [1..n].

2, 2, 5, 4, 7, 7, 10, 4, 5, 9, 14, 7, 16, 11, 11, 5, 19, 7, 22, 9, 13, 16, 26, 7, 8, 17, 6, 11, 32, 12, 35, 4, 16, 22, 15, 8, 40, 23, 19, 10, 44, 14, 47, 15, 11, 28, 50, 7, 10, 9, 23, 18, 56, 7, 19, 12, 25, 34, 62, 12, 65, 35, 13, 5

Offset: 1

James Mitchell and Wilf A. Wilson, Jul 26 2017

nonn

Wilf A. Wilson, Table of n, a(n) for n = 1..1000
James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017.

Cf. A001221, A008472.

a[1] = a[2] = 2; a[n_] := PrimeNu[n-1] + DivisorSum[n, Identity, PrimeQ]+1; Array[a, 64] (* Jean-François Alcover, Feb 18 2019 *)

a(n)= A001221(n -1) + A008472(n) + 1, n > 2.

A290140 The number of maximal subsemigroups of the Jones monoid on the set [1..n].

Original entry on oeis.org

1, 2, 5, 9, 13, 19, 27, 39, 57, 85, 129, 199, 311, 491, 781, 1249, 2005, 3227, 5203, 8399, 13569, 21933, 35465, 57359, 92783, 150099, 242837, 392889, 635677, 1028515, 1664139, 2692599, 4356681, 7049221, 11405841, 18454999, 29860775, 48315707, 78176413

Offset: 1

James Mitchell and Wilf A. Wilson, Jul 21 2017

a(2n) is the number of maximal subsemigroups of the planar partition monoid of degree n.

Wilf A. Wilson, Table of n, a(n) for n = 1..1000
James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017.
Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).

Cf. A000045.

{1, 2}~Join~Table[2 Fibonacci[n - 1] + 2 n - 3, {n, 3, 39}] (* Michael De Vlieger, Jul 21 2017 *)

Vec(x*(1 + x)*(1 - 2*x + 3*x^2 - 4*x^3 + x^4) / ((1 - x)^2*(1 - x - x^2)) + O(x^50)) \\ Colin Barker, Jul 21 2017

a(n) = 2 * A000045(n - 1) + 2n - 3, n > 2.
From Colin Barker, Jul 21 2017: (Start)
G.f.: x*(1 + x)*(1 - 2*x + 3*x^2 - 4*x^3 + x^4) / ((1 - x)^2*(1 - x - x^2)).
a(n) = -5 + (2^(-n)*((1-sqrt(5))^n*(1+sqrt(5)) + (-1+sqrt(5))*(1+sqrt(5))^n)) / sqrt(5) + 2*(1+n) for n>2.
a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) for n>6.
(End)

A290138 Number of maximal subgroups of the symmetric group S_n.

Original entry on oeis.org

0, 1, 4, 8, 22, 53, 184, 353, 1376, 3977, 363904, 396498, 39920896, 40060127, 1543910, 4687418, 1307674433536, 1307902407753, 355687428358144, 355691118382364, 162615882312376736, 1267150213999727, 51090942171713634304, 51090956256672365547

Offset: 1

James Mitchell and Wilf A. Wilson, Jul 21 2017

nonn

a(n) + 1, n > 1, is the number of maximal subsemigroups of each of the following monoids of degree n: the full transformation monoid, the symmetric inverse monoid, the dual symmetric inverse monoid, the uniform block bijection monoid, and the Brauer monoid.
a(n) + 2 is the number of maximal subsemigroups of the partial transformation monoid of degree n.
a(n) + 3, n > 1, is the number of maximal subsemigroups of the partial Brauer monoid of degree n.
a(n) + 4, n > 1, is the number of maximal subsemigroups of the partition monoid of degree n.

Wilf A. Wilson, Table of n, a(n) for n = 1..84
Utsithon Chaichompoo and Kritsada Sangkhanan, Transformation Semigroups Which Are Disjoint Union of Symmetric Groups, arXiv:2411.15081 [math.RA], 2024. See p. 10.
James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017.

Cf. A066115.

Sum(List(ConjugacyClassesMaximalSubgroups(SymmetricGroup(n)), Size));

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A290289 The number of maximal subsemigroups of the monoid of partial orientation-preserving and reversing injective mappings on the set [1..n].

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A290140 The number of maximal subsemigroups of the Jones monoid on the set [1..n].

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A290138 Number of maximal subgroups of the symmetric group S_n.

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