A383829
Number of medial involutory racks of order n, up to isomorphism.
Original entry on oeis.org
1, 1, 2, 5, 12, 38, 168, 850, 6090
Offset: 0
- Seiichi Kamada, Quandles with good involutions, their homologies and knot invariants, Intelligence of Low Dimensional Topology 2006, World Scientific Publishing Co. Pte. Ltd., 2007, pages 101-108.
- Jose Ceniceros, Mohamed Elhamdadi, and Sam Nelson, Legendrian rack invariants of Legendrian knots, Communications of the Korean Mathematical Society, 36 (2021), no. 3, 623-639.
- Lực Ta, Equivalences of racks, Legendrian racks, and symmetric racks, arXiv: 2505.08090 [math.GT], 2025.
- Lực Ta, GL-Rack Classification, GitHub, 2025.
Sequences related to racks and quandles:
A383144,
A181771,
A176077,
A179010,
A193024,
A254434,
A177886,
A196111,
A226173,
A236146,
A248908,
A165200,
A242044,
A226193,
A242275,
A243931,
A257351,
A198147,
A225744,
A226172,
A226174.
A383830
Number of Legendrian quandles of order n, up to isomorphism.
Original entry on oeis.org
1, 1, 2, 5, 15, 54, 240, 1306, 9477
Offset: 0
- Jose Ceniceros, Mohamed Elhamdadi, and Sam Nelson, Legendrian rack invariants of Legendrian knots, Communications of the Korean Mathematical Society, 36 (2021), no. 3, 623-639.
- Lực Ta, Equivalences of racks, Legendrian racks, and symmetric racks, arXiv: 2505.08090 [math.GT], 2025.
- Lực Ta, Generalized Legendrian racks: Classification, tensors, and knot coloring invariants, arXiv: 2504.12671 [math.GT], 2025.
- Lực Ta, GL-Rack Classification, GitHub, 2025.
Sequences related to racks and quandles:
A383144,
A181771,
A176077,
A179010,
A193024,
A254434,
A177886,
A196111,
A226173,
A236146,
A248908,
A165200,
A242044,
A226193,
A242275,
A243931,
A257351,
A198147,
A225744,
A226172,
A226174.
A376155
Number of prime knots with 10 or fewer crossings whose mosaic number is n.
Original entry on oeis.org
0, 1, 0, 1, 6, 96, 146
Offset: 1
There are exactly 6 prime knots that are realizable on a 5 X 5 knot mosaic but not realizable on a 4 X 4 knot mosaic. Namely, these knots are 4_1, 5_1, 5_2, 6_1, 6_2, and 7_4 (see Table 1 of Lee et al.). Hence, a(5) = 6.
- Aaron Heap, Douglas Baldwin, James Canning, and Greg Vinal, Tabulating knot mosaics: Crossing number 10 or less, arXiv: 2303.12138 [math.GT], 2023.
- Hwa Jeong Lee, Ludwig Lewis, Joseph Paat, and Amanda Peiffer, Knot mosaic tabulation, Involve, Vol. 11 (2018), pp. 13-26.
- Samuel J. Lomonaco and Louis H. Kauffman, Quantum Knots and Mosaics, Proc. Sympos. Applied Math., Amer. Math. Soc., Vol. 68 (2010), pp. 177-208.
- Index entries for sequences related to knots
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