Author

Norbert Hegyvári

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Preprint Sep 2026

Arithmetic Progressions in a Random Binary Subset-Sum Set

Let $u=(u_n)_{n\ge0}$ be a binary sequence, and define \[ X_0=1,\qquad X_{n+1}=2X_n+u_n \qquad(n\ge0). \] Let $A_u$ be the set of all nonempty finite subset sums of the sequence $(X_n)$, and let $L_u(N)$ denote the maximum length of an arithmetic progression contained in $A_u\cap[1,N]$. We prove that there are absolute...

Norbert Hegyvári, Thang Pham, Bo-Qing Xue · 0 citations

Preprint Sep 2026

Subset-Sum Density Realization in Locally Finite Abelian Groups

Let $G$ be a countable locally finite abelian group, and let \[ G_1\leq G_2\leq\cdots, \qquad \bigcup_{i\geq1}G_i=G, \] be any filtration of $G$ by finite subgroups. For $A\subseteq G$, let $\mathcal P(A)$ denote the set of all finite subset sums of elements of $A$, and let $2G:=\{2g:g\in G\}$. We prove that $|2G|=\inf...

Norbert Hegyvári, Thang Pham, Bo-Qing Xue · 0 citations