A215925 - OEIS

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A215925

The number of distinct (up to unitary similarity) *-subalgebras of the n X n complex matrices.

1, 2, 5, 10, 21, 38, 72, 124, 218, 363, 607, 977, 1580, 2479, 3889, 5976, 9162, 13812, 20771, 30811, 45561, 66638, 97117, 140237, 201811, 288119, 409904, 579240, 815715, 1141916, 1593318, 2211453, 3059662, 4213395, 5784458, 7907783, 10779202, 14636771, 19819770

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OFFSET

0,2

COMMENTS

A *-subalgebra is a subalgebra (i.e., a subspace closed under matrix multiplication) that is closed under the conjugate transpose operation.

Also the partial sums of A006171.

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..1000

William Q. Erickson, The Demazure product extended to biwords, arXiv:2407.13165 [math.CO], 2024. See p. 16.

EXAMPLE

There are 10 different (up to unitary similarity) *-subalgebras of the 3 X 3 complex matrices, which contain matrices of the following forms:

0 0 0 ... a 0 0 ... a 0 0 ... a 0 0 ... a b 0