6 papers · 1 filter
Arithmetic Progressions in a Random Binary Subset-Sum Set
Norbert Hegyvári, Thang Pham, Boqing Xue
Let be a binary sequence, and define \[ X_0=1,\qquad X_{n+1}=2X_n+u_n \qquad(n\ge0). \] Let be the set of all nonempty finite subset sums of the sequence $(…
Congruence Classes in : Sharp Results via an Energy Approach
Thang Pham, Le Quang Ham, Steven Senger +2
Let denote the set of congruence classes of ordered -tuples of pairwise distinct points of . Let be prime. For with $3\leq|…
Subset-Sum Density Realization in Locally Finite Abelian Groups
Norbert Hegyvári, Thang Pham, Boqing Xue
Let 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 by finite subgroups. For $A\subsete…
Alternative Entropy Bounds for Perfect Matchings in Bipartite Graphs
Yusong Du, Boqing Xue
We refine Radhakrishnan's entropy proof of the Brégman-Minc bound by introducing a terminal-set framework in which selected vertices are revealed last. This gives new degree-sensit…
Horizontal Kakeya maximal operators in finite Heisenberg groups: Exact exponents and applications
Thang Pham, Andrea Pinamonti, Dung The Tran +1
Let be an odd prime power. We study Kakeya maximal operators associated with horizontal lines in the finite Heisenberg groups . Our principal object i…
On the distance problem over finite p-adic rings
Thang Pham, Boqing Xue
In this paper, we study the distance problem in the setting of finite p-adic rings. In odd dimensions, our results are essentially sharp. In even dimensions, we clarify the conject…