cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A289620 Triangle read by rows: T(n,r), 0 <= r <= n, is the number of idempotents of rank r in the twisted planar partition monoid PP_n^tau.

Original entry on oeis.org

1, 0, 1, 0, 5, 1, 0, 33, 10, 1, 0, 253, 93, 15, 1, 0, 2147, 880, 178, 20, 1, 0, 19593, 8599, 1982, 288, 25, 1, 0, 188837, 86762, 21723, 3684, 423, 30, 1, 0, 1899107, 900997, 238419, 44767, 6111, 583, 35, 1, 0, 19761209, 9595264, 2638114, 531656, 81606, 9388, 768, 40, 1, 0, 211447863, 104447385, 29503900, 6255952, 1044248, 136740, 13640, 978, 45, 1
Offset: 0

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Author

James East, Oct 05 2017

Keywords

Comments

Values were computed using the Semigroups package for GAP.

Links

Crossrefs

Cf. A281441, A281442, A286867 (row sums).

A281441 Triangle read by rows: T(n,r), 0 <= r <= n, is the number of idempotents of rank r in the Jones monoid J_n.

Original entry on oeis.org

1, 0, 1, 1, 0, 1, 0, 4, 0, 1, 4, 0, 7, 0, 1, 0, 25, 0, 10, 0, 1, 25, 0, 57, 0, 13, 0, 1, 0, 196, 0, 98, 0, 16, 0, 1, 196, 0, 522, 0, 148, 0, 19, 0, 1, 0, 1764, 0, 1006, 0, 207, 0, 22, 0, 1, 1764, 0, 5206, 0, 1673, 0, 275, 0, 25, 0, 1
Offset: 0

Views

Author

James East, Oct 05 2017

Keywords

Comments

Values were computed using the Semigroups package for GAP.

Links

Crossrefs

Cf. A225798 (row sums), A281442, A289620, A001246, A016777.

Formula

T(2n,0) = T(2n+1,1) = A001246(n). T(2n+2,2n) = A016777(n). - Andrey Zabolotskiy, Oct 19 2017

A281438 Number of idempotents in the Kauffman monoid K_n.

Original entry on oeis.org

1, 1, 1, 3, 5, 15, 31, 93, 215, 653, 1619, 4979, 12949, 40293, 108517, 341241, 943937, 2996127, 8465319, 27092419, 77878271, 251073791, 732129719, 2375764351, 7012025277, 22886955207, 68254122669, 223946197065, 673885100857, 2221505541773, 6737598265009
Offset: 0

Views

Author

James East, Oct 05 2017

Keywords

Comments

The elements of K_n are pairs (i,alpha) where i is a nonnegative integer, and alpha is an element of the Jones monoid J_n. The product in K_n is defined in the Borisavljevic-Došen-Petrić article below.
Also the number of idempotent basis elements of the Temperley-Lieb algebra in the case the twisting parameter is not an M-th root of unity where M <= n.

Links

Crossrefs

Cf. A225798, A281442.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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