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User: Diego Arcis

Diego Arcis has authored 2 sequences.

A378232 Cardinality of the ramified symmetric inverse monoid R(IS_n).

1, 3, 39, 971, 38140, 2126890, 157874467, 14928602309, 1741809491235, 244735956424795, 40624759074089022, 7844197919242437824, 1739438713163799078369, 438224899712759948799899, 124286842162679198452748231, 39368769274679276781570308187, 13831693583206758886731727544652

Offset: 0

Diego Arcis, Nov 21 2024

nonn

a(n) is the number of ramified set partitions (I, J), where I is a partial permutation.

Francesca Aicardi, Diego Arcis, and Jesús Juyumaya, Ramified inverse and planar monoids, Mosc Math J, 24(3):321-355, 9 2024.

Cf. A000110.

seq(add(k!*(binomial(n, k)^2)*combinat:-bell(2*n - k),k=0..n),n=0..16); # Georg Fischer, Jun 16 2025

a(n) = Sum_{k=0..n}(k!*(binomial(n, k)^2)*A000110(2n - k)).

a(10)-a(16) corrected by Georg Fischer, Jun 16 2025

A370758 Number of ramified partitions (I,J) of size n, where J is balanced with respect to up brackets and down brackets.

Original entry on oeis.org

1, 1, 5, 48, 747, 17040, 531810, 21634515, 1107593235, 69482175840, 5229801016650, 464302838867175, 47939015445032250, 5688437019459319125, 767922887039461928775, 116915022542869964287875, 19922514312608630279431875, 3774243527942494591068084000, 790220453914362566924533955250

Offset: 0

Diego Arcis, Feb 29 2024

nonn

a(n) is the cardinality of the balanced ramified Brauer monoid bBr_n.

			a(3) = 48 is the number of ramified partitions (I,J) of size 3, in which each block of J contains the same number of up brackets and down brackets from I, i.e., each block of J contains either no brackets from I or one up and one down bracket from I.

Diego Arcis, Table of n, a(n) for n = 0..200
Francesca Aicardi, Diego Arcis, and Jesús Juyumaya, Brauer and Jones tied monoids, arXiv:2107.04170 [math.RT], 2021.
Francesca Aicardi, Diego Arcis, and Jesús Juyumaya, Brauer and Jones tied monoids, J. Pure. Appl. Algebra 227 (2023), 107161.

Cf. A343254.

a(n) = Sum_{k=0..n/2} n!^2/(2^(2*k)*k!^2*(n-2*k)!) * A343254(n,k).

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User: Diego Arcis

A378232 Cardinality of the ramified symmetric inverse monoid R(IS_n).

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