HUN-REN Alfréd Rényi Institute of Mathematics

A superlinear improvement on line-free sets in Fp3

Building on an earlier result of the author together with Elsholtz, Führer, Füredi, Pach, Simon and Velich, we present an improved construction for a line-free set in 𝔽 3 𝑝 , having size at least ( 𝑝 − 1 ) 3 + 1 8 ⁢ 𝑝 3 / 2 − 𝑂 ⁡ ( 𝑝 ) as 𝑝 → ∞ . This results in a superlinear-ter...

Multivalued forbidden numbers of two-rowed configurations -- the missing cases

The present paper considers extremal combinatorics questions in the language of matrices. An $s$-matrix is a matrix with entries in $\{0,1,\ldots, s-1\}$. An $s$-matrix is simple if it has no repeated columns. A matrix $F$ is a configuration in a matrix $A$, denoted $F\prec A$, i...

Moser–Tardos Algorithm with small number of random bits

We study a variant of the parallel Moser–Tardos Algorithm. We prove that if we restrict attention to a class of problems whose dependency graphs have subexponential growth, then the expected total number of random bits used by the algorithm is constant; in particular, it is indep...

Fractal zeta functions for $$p$$-adic affine variaties

Abstract We investigate the fractal zeta function of a $$p$$ p -adic affine variety. We identify it with the distance zeta function. We also prove that for smooth varieties with good reduction it is a rational function of $t=p^{-s}$ t = p - s and that the abscissa of convergence...

Estimating the convex relaxation of the ideal magnetohydrodynamics equations

We investigate the explicit convex relaxation of the ideal magnetohydrodynamics equations. We provide a non-trivial lower estimate on the lamination hull and an upper estimate on the Λ-convex hull, the latter providing inequalities which will be satisfied by weak limits of weak s...

Small units in CNS

Abstract Let $$\mathbb{K}$$ K be an algebraic number field of degree $$k$$ k with a canonical number system $$(\alpha, \mathcal{N})$$ ( α , N ) . Denote $$S$$ S a finite set of places of $$ \mathbb{K}$$ K including the archimedean places and such that there is a place $$v\in M_\m...

Minimizing cutting costs in 1D rod cutting

Abstract We study a one‐dimensional rod‐cutting problem arising from an industrial setting where cutting itself carries cost . Each order specifies a length interval, and the task is to assign orders to warehouse rods so that all orders are satisfied while the number of cuts is m...

A new adaptive two-layer model for opinion spread in hypergraphs: parameter sensitivity and estimation

In studies of opinion spread, peer pressure is often modeled through interactions of more than two individuals (higher-order interactions). We introduce a two-layer random hypergraph model, in which households and workplaces form the layers and hyperedges represent individual hou...

Softening Locally Polyhedral Tilings

Abstract We call a cell $$C \subset \mathbb {R}^d$$ C ⊂ R d soft if every point of its boundary lies on a smooth curve contained in $$\partial C$$ ∂ C . A tiling of the space is called completely soft if all of its cells are soft. In their 2024 article, Domokos, Goriely, G. Horvá...

A complete dichotomy theorem on the sparse t-uniform hypergraphicality problem

We prove a complete dichotomy theorem for the parameterized sparse t -uniform hypergraphical degree sequence problem, sparse - t - uni - HDS α ′ , α . For any fixed t ≥ 3 , given parameters 0 ≤ α ′ ≤ α < t − 1 , the input consists of degree sequences D of length n with degrees be...

Simultaneous Network Design With Restricted Link Usage

ABSTRACT Given a digraph with two terminal vertices and as well as a conservative cost function and several not necessarily disjoint color classes on its arc set, our goal is to find a minimum‐cost subset of the arcs such that its intersection with each color class contains an ‐...

RESTRICTED PARTITION FUNCTIONS AND ADDITIVE COMPLEMENTS

Abstract Let N ${\mathbb N}$ double struck upper N be the set of positive integers. For subsets A , M ⊆ N $\mathcal {A},\mathcal {M}\subseteq {\mathbb N}$ script upper A comma script upper M subset of or equal to double struck upper N and n ∈ N $n\in {\mathbb N}$ n element of dou...

A bound on the equivariant unknotting number

Abstract We study how the equivariant signature of strongly invertible knots changes when one of the Boyle–Chen equivariant crossing change moves is applied. It follows from our results that the absolute value of the equivariant signature introduced by Alfieri–Boyle gives a lower...

Multiscale patterns of migration flows in Austria: regionalization, administrative barriers, and urban-rural divides

Abstract Migration is central to various societal problems related to socioeconomic development. While much of the existing research has focused on international migration, migration patterns within a single country remain relatively unexplored. In this work, we study internal mi...

Nordhaus–Gaddum‐Type Theorems for Maximum Average Degree

ABSTRACT A ‐decomposition of a graph is a partition of its edge set into spanning subgraphs . The classical theorem of Nordhaus and Gaddum bounds and over all 2‐decompositions of . For a graph parameter , let , taken over all ‐decompositions of graph . In this paper, we consider...

Revisiting the Stability of the Ingleton Inequality: A Tropicalization-Free Approach

The classical Ingleton inequality is known to hold for entropic points under specific exact conditional independence constraints. Recently, Matveev and Romashchenko (2026) investigated the stability of these implications, quantifying the extent to which the Ingleton inequality ca...

On the connection between zero-free regions and the error term in the prime number theorem

Abstract We provide for a wide class of zero-free regions an upper bound for the error term in the Prime Number Theorem, refining works of Pintz (1980), Johnston (2024), and Révész (2024). Our method does not only apply to the Riemann zeta function, but to general Beurling zeta f...