A038719 -id:A038719 - cp's OEIS frontend

A330032 The number of chains of strictly rooted upper triangular or lower triangular matrices of order n.

1, 2, 26, 9366, 204495126, 460566381955706, 162249649997008147763642, 12595124129900132067036747870669270, 288398561903310939256721956218813835167026180310, 2510964964470962082968627390938311899485883615067802615950711482

Offset: 0

S. R. Kannan, Rajesh Kumar Mohapatra, Feb 29 2020

nonn

Also, the number of chains in the power set of (n^2-n)/2-elements such that the first term of the chains is either an empty set or a set of (n^2-n)/2-elements.
The number of rooted chains of 2-element subsets of {0,1, 2, ..., n} that contain no consecutive integers.
The number of distinct rooted reflexive symmetric fuzzy matrices of order n.
The number of chains in the set consisting of all n X n reflexive symmetric matrices such that the first term of the chains is either reflexive symmetric matrix or unit matrix.

Alois P. Heinz, Table of n, a(n) for n = 0..28
S. R. Kannan and Rajesh Kumar Mohapatra, Counting the Number of Non-Equivalent Classes of Fuzzy Matrices Using Combinatorial Techniques, arXiv preprint arXiv:1909.13678 [math.GM], 2019.
R. B. Nelsen and H. Schmidt, Jr., Chains in power sets, Math. Mag., 64 (1) (1991), 23-31.
M. Tărnăuceanu, The number of chains of subgroups of a finite elementary abelian p-group, arXiv preprint arXiv:1506.08298 [math.GR], 2015.

Cf. A000629, A038719, A007047, A328044, A330301, A330302, A330804, A331957.

a(n) = A000629((n^2-n)/2).

Missing term a(6) = 162249649997008147763642 inserted by Georg Fischer, Jul 15 2024

A329712 The number of rooted chains in the lattice of (0, 1) matrices of order n.

Original entry on oeis.org

1, 2, 150, 14174522, 10631309363962710, 213394730876951551651166996282, 288398561903310939256721956218813835167026180310, 55313586130829865212025793302979452922870356482030868613037427298852922

Offset: 0

S. R. Kannan, Rajesh Kumar Mohapatra, Feb 29 2020

nonn

Also, the number of n X n distinct rooted fuzzy matrices.
The number of chains in the power set of n^2-elements such that the first term of the chains is either an empty set or a set of n^2-elements.
The number of chains in the collection of all binary (crisp or Boolean or logical) matrices of order n such that the first term of the chains is either null matrix or unit matrix.

S. R. Kannan and Rajesh Kumar Mohapatra, Counting the Number of Non-Equivalent Classes of Fuzzy Matrices Using Combinatorial Techniques, arXiv preprint arXiv:1909.13678 [math.GM], 2019.
V. Murali and B. Makamba, Finite Fuzzy Sets, Int. J. Gen. Syst., Vol. 34 (1) (2005), pp. 61-75.
R. B. Nelsen and H. Schmidt, Jr., Chains in power sets, Math. Mag., 64 (1) (1991), 23-31.
M. Tărnăuceanu, The number of chains of subgroups of a finite elementary abelian p-group, arXiv preprint arXiv:1506.08298 [math.GR], 2015.

Cf. A000629, A038719, A007047, A328044, A330301, A330302, A330804, A331957.

a(n) = A000629(n^2).

A329911 The number of rooted chains of reflexive matrices of order n.

Original entry on oeis.org

1, 1, 6, 9366, 56183135190, 5355375592488768406230, 22807137588023760967484928392369803926, 9821625950779149908637519199878777711089567893389821437206

Offset: 0

S. R. Kannan, Rajesh Kumar Mohapatra, Feb 29 2020

nonn

Also, the number of n X n distinct rooted reflexive fuzzy matrices.
The number of chains in the power set of (n^2-n)-elements such that the first term of the chains is either an empty set or a set of (n^2-n)-elements.
The number of chains in the collection of all reflexive matrices of order n such that the first term of the chains is either identity matrix or unit matrix.

S. R. Kannan and Rajesh Kumar Mohapatra, Counting the Number of Non-Equivalent Classes of Fuzzy Matrices Using Combinatorial Techniques, arXiv preprint arXiv:1909.13678 [math.GM], 2019.
V. Murali, Combinatorics of counting finite fuzzy subsets, Fuzzy Sets Syst., 157(17)(2006), 2403-2411.
M. Tărnăuceanu, The number of chains of subgroups of a finite elementary abelian p-group, arXiv preprint arXiv:1506.08298 [math.GR], 2015.

Cf. A000629, A038719, A007047, A328044, A330301, A330302, A330804, A331957.

a(n) = A000629(n^2-n).

cp's OEIS Frontend

A330032 The number of chains of strictly rooted upper triangular or lower triangular matrices of order n.

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A329712 The number of rooted chains in the lattice of (0, 1) matrices of order n.

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A329911 The number of rooted chains of reflexive matrices of order n.

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