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

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

Offset: 0

Author

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

Keywords

• nonn

Comments

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.

Links

• 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.

Crossrefs

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

Formula

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