Affine vector space partitions

نویسندگان

چکیده

Abstract An affine vector space partition of $${{\,\textrm{AG}\,}}(n,q)$$ AG ( n , q ) is a set proper subspaces that partitions the points. Here we determine minimum sizes and enumerate equivalence classes for small parameters. We also give parametric constructions arbitrary field sizes.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Affine Partitions and Affine Grassmannians

We give a bijection between certain colored partitions and the elements in the quotient of an affine Weyl group modulo its Weyl group. By Bott’s formula these colored partitions give rise to some partition identities. In certain types, these identities have previously appeared in the work of Bousquet-Melou-Eriksson, Eriksson-Eriksson and Reiner. In other types the identities appear to be new. F...

متن کامل

More On Embedding an Affine Space in a Vector Space

for all a1 . . . , am ∈ E, all v1, . . . , vm ∈ −→E , and all λ1, . . . , λm ∈ R. Furthermore, for λi = 0, 1 ≤ i ≤ m, we have f̂(v1 +̂ λ1a1, . . . , vm +̂ λmam) = λ1 · · ·λmf(a1 + λ−1 1 v1, . . . , am + λ−1 m vm). Proof . Let us assume that f̂ exists. We first prove by induction on k, 1 ≤ k ≤ m, that f̂(a1, . . . , vi1 , . . . , vik , . . . , am) = fS(vi1 , . . . , vik), for every S ⊆ {1, . . . ,m},...

متن کامل

On vector space partitions and uniformly resolvable designs

Let Vn(q) denote a vector space of dimension n over the field with q elements. A set P of subspaces of Vn(q) is a partition of Vn(q) if every nonzero vector in Vn(q) is contained in exactly one subspace in P. A uniformly resolvable design is a pairwise balanced design whose blocks can be resolved in such a way that all blocks in a given parallel class have the same size. A partition of Vn(q) co...

متن کامل

Counting the Restricted Gaussian Partitions of a Finite Vector Space

A subspace partition Π of a finite vector space V = V (n, q) of dimension n over GF(q) is a collection of subspaces of V such that their union is V , and the intersection of any two subspaces in Π is the zero vector. The multiset TΠ of dimensions of subspaces in Π is called the type of Π, or, a Gaussian partition of V . Previously, we showed that subspace partitions of V and their types are nat...

متن کامل

Vector Space semi-Cayley Graphs

The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Designs, Codes and Cryptography

سال: 2023

ISSN: ['0925-1022', '1573-7586']

DOI: https://doi.org/10.1007/s10623-023-01263-z