Counting Packings of Generic Subsets in Finite Groups
نویسنده
چکیده
A packing of subsets S1, . . . ,Sn in a group G is an element (g1, . . . , gn) of Gn such that g1S1, . . . , gnSn are disjoint subsets of G. We give a formula for the number of packings if the group G is finite and if the subsets S1, . . . ,Sn satisfy a genericity condition. This formula can be seen as a generalization of the falling factorials which encode the number of packings in the case where all the sets Si are singletons.
منابع مشابه
Harmonic Analysis, Ergodic Theory and Counting for Thin Groups
For a geometrically finite group Γ of G = SO(n, 1), we survey recent developments on counting and equidistribution problems for orbits of Γ in a homogeneous space H\G where H is trivial, symmetric or horospherical. Main applications are found in an affine sieve on orbits of thin groups as well as in sphere counting problems for sphere packings invariant under a geometrically finite group. In ou...
متن کاملMaximal subsets of pairwise non-commuting elements of some finite p-groups
Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...
متن کاملPairwise non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups
Let $G$ be a finite group. A subset $X$ of $G$ is a set of pairwise non-commuting elements if any two distinct elements of $X$ do not commute. In this paper we determine the maximum size of these subsets in any finite non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup.
متن کاملA relation between infinite subsets and exterior center in groups
Let G be a group. Neumann to answer a question of Paul Erdos proved that every infinite subset of G has two different comuting elements if and only if G is center-by-finite. In this paper, we deal with Erdoschr('39')s question in different aspect and we show that every infinite subset X of G has two different elements x and y such that x^y=1 if and only if the exterior center of G ihas finit...
متن کاملDense packings from algebraic number fields and codes
We introduce a new method from number fields and codes to construct dense packings in the Euclidean spaces. Via the canonical Q-embedding of arbitrary number field K into R, both the prime ideal p and its residue field κ can be embedded as discrete subsets in R. Thus we can concatenate the embedding image of the Cartesian product of n copies of p together with the image of a length n code over ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 19 شماره
صفحات -
تاریخ انتشار 2012