We give conditions for k‐point configuration sets of thin sets to have nonempty interior,
applicable to a wide variety of configurations. This is a continuation of our earlier work (J …

Let 𝔽 qd be the d-dimensional vector space over the finite field 𝔽 q with q elements. For
each non-zero r in 𝔽 q and E⊂ 𝔽 qd, we define W⁢(r) as the number of quadruples (x, y, z …

Let F q be a finite field of order q and E be a set in F q d. The distance set of E is defined by Δ
(E):={‖ x− y‖: x, y∈ E}, where‖ α‖= α 1 2+…+ α d 2. Iosevich, Koh and Parshall (2018) …

In this paper, we study problems about the similar configurations in F q d. Let G=(V, E) be a
graph, where V={1, 2,…, n} and E⊆(V 2). For a set E in F qd, we say that E contains a pair of …

Abstract Let $\mathbb {F} _q^ d $ denote the d-dimensional vector space over the finite field
$\mathbb {F} _q $ with q elements. Define for $\alpha=(\alpha _1,\dots,\alpha _d)\in\mathbb …

In 2017, by using the group theoretic approach and tools from discrete Fourier analysis,
Bennett, Hart, Iosevich, Pakianathan, and Rudnev obtained a number of results on the …

Abstract Let ϕ (x, y): ℝ d× ℝ d→ ℝ ϕ(x,y):R^d*R^d→R be a function. We say ϕ is a Mattila–
Sjölin type function of index γ if γ is the smallest number satisfying the property that for any …

Let $ E\subset\mathbb {F} _q^ d $ and $\lVert\cdot\rVert:\mathbb {F} _q^ d\to\mathbb {F} _q $
defined as $\lVert\alpha\rVert:=\alpha_1^ 2+\dots+\alpha_d^ 2$ if $\alpha=(\alpha_1,\dots …

In this paper, we study problems about the similar configurations in $\mathbb {F} _q^ d $. Let
$ G=(V, E) $ be a graph, where $ V=\{1, 2,\ldots, n\} $ and $ E\subseteq {V\choose2} $. For a …

Let $\mathbb {F} _q $ denote the finite field of $ q $ elements. For $ E\subset\mathbb {F} _q^
d $, denote the distance set $\Delta (E)=\{\| xy\|^ 2:=(x_1-y_1)^ 2+\cdots+(x_d-y_d)^ 2:(x …