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 1-2 of 2 results.

A383831 Number of medial Legendrian quandles of order n, up to isomorphism.

Original entry on oeis.org

1, 1, 2, 5, 14, 48, 219, 1207, 9042
Offset: 0

Views

Author

Luc Ta, May 16 2025

Keywords

Comments

A rack or quandle is medial if it satisfies the identity (xy)(uv) = (xu)(yv).
A Legendrian quandle is a pair (X,u) where X is a quandle and u is an involutory automorphism of X such that u(yx)=y(u(x)); see Ta, "Generalized Legendrian...," Corollary 3.13.
a(n) is also the number of medial racks X such that the kink map X -> X defined by x -> x(x) is an involution; see Ta, "Equivalences of...," Theorem 1.1.

Links

Crossrefs

Cf. A383828-A383830, A383145, A383146, A181769, A181770, A178432.
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.
Sequences related to Legendrian knots: A374939, A374942, A374943, A374944, A374945, A374946, A374947.

Programs

  • GAP
    # See Ta, GitHub link

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

Views

Author

Luc Ta, May 11 2025

Keywords

Comments

A rack is involutory if it satisfies the identity y(yx) = x. In particular, involutory quandles are called kei.
A rack is medial if it satisfies the identity (xy)(uv) = (xu)(yv).
a(n) is also the number of medial Legendrian kei (i.e., medial kei equipped with Legendrian structures) up to order n up to isomorphism; see Ta, Theorem 1.1.
a(n) is also the number of medial symmetric kei (i.e., medial kei equipped with good involutions) up to order n up to isomorphism; see Ta, "Equivalences of...," Corollary 1.3.

References

  • 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.

Links

Crossrefs

Cf. A383828, A383830, A383831, A383145, A383146, A181769, A181770, A178432.
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.
Sequences related to Legendrian knots: A374939, A374942, A374943, A374944, A374945, A374946, A374947.

Programs

  • GAP
    # See Ta, GitHub link
Showing 1-2 of 2 results.

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