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Constructive Combinatorics in Elementary School Mathematics
AbstractThe paper describes in detail a class of educational problems from an elementary school course of mathematics and computer science. This...
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Distributed algorithms, the Lovász Local Lemma, and descriptive combinatorics
In this paper we consider coloring problems on graphs and other combinatorial structures on standard Borel spaces. Our goal is to obtain sufficient...
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Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures Foundations and Applications
This book gathers invited, peer-reviewed works presented at the 2021 edition of the Classical and Constructive Nonassociative Algebraic Structures:...
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Reverse Mathematics
Reverse mathematics is a new take on an old idea: asking which axioms are necessary to prove a given theorem. This question was first asked about the...
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Problematic of Mathematics, Social Sciences, and Arts: A Ubiquitous Constructive Interaction in Algebraic Modeling
In this opening chapter, we reflect on the nature of mathematics and its contribution to society through two important ways of doing mathematics:...
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The Mathematics of László Lovász
This is an exposition of the contributions of László Lovász to mathematics and computer science written on the occasion of the bestowal of the Abel...
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The research and progress of the enumeration of lattice paths
The enumeration of lattice paths is an important counting model in enumerative combinatorics. Because it can provide powerful methods and technical...
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Ramsey Theory
Ramsey theory is a branch of combinatorics that asks questions of the form: How large must a set be so that if it is divided into subsets, at least...
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Sum Index, Difference Index and Exclusive Sum Number of Graphs
We consider two recent conjectures made by Harrington, Henninger-Voss, Karhadkar, Robinson and Wong concerning relationships between the sum index,...
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Full ellipsoid embeddings and toric mutations
This article introduces a new method to construct volume-filling symplectic embeddings of 4-dimensional ellipsoids by employing polytope mutations in...
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Consensus in Asynchronous Multiagent Systems. III. Constructive Stability and Stabilizability
We describe certain classes of linear asynchronous multi-agent systems in discrete time for which the stability problem allows for a constructive...
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Newton Polyhedra and Stratified Resolution of Singularities in the Class of Generalized Power Series
We generalize the construction of a toric variety associated with an integer convex polyhedron to construct generalized analytic varieties associated...
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Reconstruction of Parameters of a Set of Radiant Points from Their Images
AbstractWithin the framework of geometric tomography, inverse problems of photometry, wave optics, and discrete tomography, we study questions on...
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Reverse Mathematics
Reverse mathematics is a new take on an old idea: asking which axioms are necessary to prove a given theorem. This question was first asked about the...
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Kolmogorov Complexity as a Combinatorial Tool
Kolmogorov complexity is often used as a convenient language for counting and/or probabilistic existence proofs. However, there are some applications...
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A note on residual allocation models
Residual allocation models (RAMs) arise in many subjects including Bayesian statistics, combinatorics, ecology, finance, information theory, machine...
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Combinatorics Encoding Geometry: The Legacy of Bill Thurston in the Story of One Theorem
This chapter presents a whirlwind tour of some results surrounding the Koebe–Andre’ev–Thurston Theorem, Bill Thurston’s seminal circle packing...
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Near-sunflowers and focal families
We present some problems and results about variants of sunflowers in families of sets. In particular, we improve an upper bound of the first author,...