A179543 Small values of the index immediately eliminated by a lemma arising in well-rounded sublattices of the hexagonal lattice.

2, 5, 6, 10, 11, 14, 17, 22, 23, 26, 29, 33, 34, 38, 41, 46, 47, 53, 59

Offset

1,1

Comments

Given from Lemma 5.5, p.17 of Fukshansky. Abstract: We produce an explicit parameterization of well-rounded sublattices of the hexagonal lattice in the plane, splitting them into similarity classes. We use this parameterization to study the number, the greatest minimal norm, and the highest signal-to-noise ratio of well-rounded sublattices of the hexagonal lattice of a fixed index. This investigation parallels earlier work by Bernstein, Sloane, and Wright where similar questions were addressed on the space of all sublattices of the hexagonal lattice. Our restriction is motivated by the importance of well-rounded lattices for discrete optimization problems. Finally, we also discuss the existence of a natural combinatorial structure on the set of similarity classes of well-rounded sublattices of the hexagonal lattice, induced by the action of a certain matrix monoid.

Links

Table of n, a(n) for n=1..19.

Lenny Fukshansky, Daniel Moore, R. Andrew Ohana and Whitney Zeldow, On well-rounded sublattices of the hexagonal lattice, Discrete Math. 310 (2010), no. 23, 3287-3302.

Crossrefs

Sequence in context: A183987 A187840 A187904 * A077471 A273324 A238096

Adjacent sequences: A179540 A179541 A179542 * A179544 A179545 A179546

Keyword

more,nonn

Author

Jonathan Vos Post, Jul 18 2010

Status

approved