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

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

Offset: 0

Author

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

Keywords

• nonn

Comments

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.

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, 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.

Crossrefs

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

Formula

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