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On the inequalities of Turán, Bernstein and Erdős–Lax in quaternionic setting
In this paper we study the extensions of the classical inequalities of Bernstein, Erdős–Lax and Turán’s inequalities, from complex polynomials to...
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On key applications of the Turán–Kubilius inequality
After briefly describing the origin and the scope of the Turán–Kubilius inequality, we show how this important inequality leads to the law of large...
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The Turán-type inequality in the space L0 on the unit interval
Let P ( x ) be an arbitrary algebraic polynomial of degree n with all zeros in the unit interval −1 ≤ x ≤ 1. We establish the Turán-type inequality ‖ P″ ‖ 0 ...
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On the density theorem of Halász and Turán
Gábor Halász and Pál Turán were the first who proved unconditionally the Density Hypothesis for Riemann’s zeta function in a fixed strip
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A Hypergraph Turán Problem with No Stability
A fundamental barrier in extremal hypergraph theory is the presence of many near-extremal constructions with very different structures. Indeed, the...
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Estimates of the Number of Edges in Subgraphs of Johnson Graphs
AbstractWe consider special distance graphs and estimate the number of edges in their subgraphs. The estimates obtained improve some known...
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Continuous cubic formulations for cluster detection problems in networks
The celebrated Motzkin–Straus formulation for the maximum clique problem provides a nontrivial characterization of the clique number of a graph in...
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Localised Graph Maclaurin Inequalities
The Maclaurin inequalities for graphs are a broad generalisation of the classical theorems of Turán and Zykov. In a nutshell they provide an...
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A remark on density theorems for Riemann’s zeta-function
The goal of this paper is to give a relatively simple proof of some known zero density estimates for Riemann’s zeta-function which are sufficiently...
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Connection Between Continuous Optimization and Turán Densities of Non-uniform Hypergraphs
A classical result of Motzkin and Straus established the connection between the Lagrangian of a graph and its maximum cliques. Applying it, they gave...
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The Happy End Problem
During the winter of 1932–1933, two young friends, mathematics student Paul (Pál) Erdős, aged 19, and chemistry student George (György) Szekeres, 21,...
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A Tensor Optimization Algorithm for Computing Lagrangians of Hypergraphs
The Lagrangian of a hypergraph is a crucial tool for studying hypergraph extremal problems. Though Lagrangians of some special structure hypergraphs,...
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On the Minimal Number of Edges in Induced Subgraphs of Special Distance Graphs
AbstractThree new theorems are proved in the paper, which give bounds for the number of edges in induced subgraphs of a special distance graph.
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Large Independent Sets from Local Considerations
The following natural problem was raised independently by Erdős–Hajnal and Linial–Rabinovich in the early ’90 s. How large must the independence...
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Remez-Type Inequalities and Their Applications
Polynomial inequalities on measurable sets play an important rôle in many areas of analysis. In particular, Remez [16] established the following...