Counting Co-Cyclic Lattices
نویسندگان
چکیده
Abstract. There is a well-known asymptotic formula, due to W. M. Schmidt (1968) for the number of full-rank integer lattices of index at most V in Z. This set of lattices L can naturally be partitioned with respect to the factor group Z/L. Accordingly, we count the number of full-rank integer lattices L ⊆ Z such that Z/L is cyclic and of order at most V , and deduce that these co-cyclic lattices are dominant among all integer lattices: their natural density is (ζ(6) ∏n
منابع مشابه
On the Geometry of Cyclic Lattices
Cyclic lattices are sublattices of ZN that are preserved under the rotational shift operator. Cyclic lattices were introduced by D. Micciancio in [16] and their properties were studied in the recent years by several authors due to their importance in cryptography. In particular, Peikert and Rosen [19] showed that on cyclic lattices in prime dimensions, the shortest independent vectors problem S...
متن کاملPermutation invariant lattices
We say that a Euclidean lattice in Rn is permutation invariant if its automorphism group has non-trivial intersection with the symmetric group Sn, i.e., if the lattice is closed under the action of some non-identity elements of Sn. Given a fixed element τ ∈ Sn, we study properties of the set of all lattices closed under the action of τ : we call such lattices τ -invariant. These lattices natura...
متن کاملOn generalized topological molecular lattices
In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices, topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...
متن کاملCounting Finite Residuated Lattices
We study finite residuated lattices with up to 11 elements. We present an algorithm for generating all non-isomorphic finite residuated lattices with a given number of elements. Furthermore, we analyze selected properties of all the lattices generated by our algorithm and present summarizing statistics.
متن کاملTransversal Lattices
A flat of a matroid is cyclic if it is a union of circuits; such flats form a lattice under inclusion and, up to isomorphism, all lattices can be obtained this way. A lattice is a Tr-lattice if all matroids whose lattices of cyclic flats are isomorphic to it are transversal. We investigate some sufficient conditions for a lattice to be a Tr-lattice; a corollary is that distributive lattices of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 30 شماره
صفحات -
تاریخ انتشار 2016