A281438 Number of idempotents in the Kauffman monoid K_n.

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

Author

James East, Oct 05 2017

Keywords

• nonn

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

• Mirjana Borisavljević, Kosta Došen, and Zoran Petrić, Kauffman monoids, arXiv:math/0008187 [math.GT], 2000-2001; J. Knot Theory Ramifications, 11(2):127-143, 2002.
• Igor Dolinka, James East, Athanasios Evangelou, Desmond FitzGerald, Nicholas Ham, James Hyde, Nicholas Loughlin, Idempotent Statistics of the Motzkin and Jones Monoids, arXiv:1507.04838 [math.CO], 2015-2016.
• James D. Mitchell, C++ code to compute the sequence

Crossrefs

Cf. A225798, A281442.