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An effective local-global principle and additive combinatorics in finite fields
We use recent results about linking the number of zeros on algebraic varieties over ℂ, defined by polynomials with integer coefficients, and on their...
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Coefficient Asymptotics of Algebraic Multivariable Generating Functions
Analytic combinatorics in several variables (ACSV) seeks to extract the asymptotic behavior of coefficients from a generating function in several...
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A survey of semisimple algebras in algebraic combinatorics
This is a survey of semisimple algebras of current interest in algebraic combinatorics, with a focus on questions which we feel will be new and...
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Geometry and Combinatorics via Right-Angled Artin Groups
We survey the relationship between the combinatorics and geometry of graphs and the algebraic structure of right-angled Artin groups. We concentrate...
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Poincaré–Reeb graphs of real algebraic domains
An algebraic domain is a closed topological subsurface of a real affine plane whose boundary consists of disjoint smooth connected components of real...
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Stationary Points at Infinity for Analytic Combinatorics
On complex algebraic varieties, height functions arising in combinatorial applications fail to be proper. This complicates both the description and...
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Combinatorics of type D Exceptional Sequences
Exceptional sequences are important sequences of quiver representations in the study of representation theory of algebras. They are also closely...
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Extensions of Some Known Algebraic and Combinatorial Identities
By means of a general partial fraction decomposition expression, we will derive several striking algebraic and combinatorial identities including...
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Combinatorics Arising from Lax Colimits of Posets
In this paper we study maximal chains in certain lattices constructed from powers of chains by iterated lax colimits in the 2-category of posets....
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Pseudospheres: combinatorics, topology and distributed systems
Pseudospheres are simplicial complexes defined in the late 1990s to model some aspects of distributed systems. Since then, combinatorial properties...
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Combinatorics
This chapter presents a collection of theorems in combinatorics, proved in the twenty-first century, which are at the same time great and easy to...
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Algebraic Preliminaries
In this chapter, we review some facts from abstract algebra. Since we assume that the reader is familiar with basic abstract algebra, we put the...
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Lacunary series, algebraic normal forms, convolutions
Conditions are found on an operation on a finite set for its transform to be lacunary, that is, missing many expected terms. Often the condition is...
