دانلود کتاب Combinatorial and Additive Number Theory V: CANT, New York, USA, 2021 (Springer Proceedings in Mathematics & Statistics, 395)

فهرست مطالب :

Preface: Mathematics in the Time of COVID
Contents
On the Number of Dot Product Chains in Finite Fields and Rings
1 Introduction
Background
Notation
Main Results
Sharpness and Relevance of Hypotheses
2 Bounds on 3-Chains in mathbbFqd
3 Bounds on k-Chains in mathbbZqd
4 Bounds on k-chains in mathbbFqd
5 Small Set Results
Proof of Theorem 4
Erratum
References
Completeness of Positive Linear Recurrence Sequences
1 Introduction
2 Modifying Sequences
Maximal Complete Sequence
Modifications of Sequences of Arbitrary Coefficients
3 Families of Sequences
Using 1s and 0s as Initial Coefficients
The ``2L—1 Conjecture\'\'
4 An Analytical Approach
An Introduction to Principal Roots
Applications to Completeness
Denseness of Incomplete Roots
5 Open Questions
6 Brown\'s Criterion and a Corollary
7 Lemmas for Sect.2
8 Lemmas for Sect.3
9 Lemmas for Sect.4
References
Length Density and Numerical Semigroups
1 Introduction
2 Background
3 Asymptotics and Computation
4 Families of Numerical Semigroups
Supersymmetric Numerical Semigroups
Embedding Dimension 3 Numerical Semigroups
Maximal Embedding Dimension Numerical Semigroups
5 Tasty and Bland Gluings of Numerical Semigroups
References
On a Problem of Cilleruelo and Nathanson, II
1 Introduction
2 Proof of Theorem 1
3 Proof of Theorem 2
References
Linked Partition Ideals and a Schur-Type Identity of Andrews
1 Introduction
2 Linked Partition Ideals and a Matrix Equation
3 q-Borel Operators
4 Non-standard Generating Function
5 Theorem 1
6 The Continuous q-Hermite Polynomials
References
Semi-magic Matrices for Dihedral Groups
1 Introduction
2 Definitions and Notations
3 Structure of D2n
4 Irreducible Types for ρ
5 The Intertwining Operator ρ
6 Semi-magic Matrices
7 Semi-magic Squares for MM(D2n)
8 Alternative Counting Formulas
9 Orthogonal Idempotents for MM(D2n)
10 Quaternionic Bases
References
Is the Syracuse Falling Time Bounded by 12?
1 Introduction
2 Falling Time Records
Integers Satisfying `3́9`42`\"̇613A``45`47`\"603Aft(n) > 14
Glide Records
Falling Time Distribution
A Variant of Jumps
3 The Syracuse Version
Current Maximum
A Variant of Syracuse Jumps
4 The Case 2ell-1
5 For Very Large n
Heuristics
A Challenge
References
Genera of Numerical Semigroups and Polynomial Identities for Degrees of Syzygies
1 Introduction
2 Polynomial Identities for Numerical Semigroups
Polynomial Identities of Arbitrary Degree
Derivatives Φ(r)z=1, Ψ(r)z=1 and Π(r) z=1
3 Linear Equations for Alternating Power Sums mathbbCk(Sm)
4 Algebraic Equations for Kr in Numerical Semigroups
Numerical Semigroups S3
5 Supplementary Relations for Kr and Gr in Symmetric Semigroups
Symmetric (Not CI) Numerical Semigroups S4
Supplementary Relations for Kr and Gr in Symmetric CI Semigroups
6 Concluding Remarks
References
Lp Estimates for Bilinear Generalized Radon Transforms in the Plane
1 Introduction
2 A General Class of Bilinear Generalized Radon Transforms
3 Sharpness Examples
4 Summary of Sharpness Conditions and Vertices of Q(Bθ)
5 Trivial Bounds
6 The L32 timesL32 toL1 Estimate for the Model Operators
7 The L2,1 timesL2,1 toL2 Estimate for the Model Operators, 0<θ<π
8 The L32 timesL32 toL1 Estimate for General Operators
9 The L2,1timesL2,1toL2 Estimate for General Operators
10 Comparison with Loomis-Whitney Conditions
References
Expansion, Divisibility and Parity: An Explanation
1 Introduction
2 A First Attempt
3 Graphs, Operators and Eigenvalues
4 Main Part of the Proof: Counting Closed Walks
5 Conclusions
References
Sums of Squares: Methods for Proving Identity Families
1 Motivation
2 Examples
3 Main Theorem: Statement and Proof Outline
4 The Seven Coefficient Groups
5 Detailed Outline of Proof
6 The Five Summands
7 Index Tables for Summand-I Through Summand-V
8 Distribution of Ni,j Across Index Sets
9 Conclusion
References
Generalized Bernoulli Numbers, Cotangent Power Sums, and Higher-Order Arctangent Numbers
1 Introduction
2 Proofs
References
A New Class of Minimal Asymptotic Bases
1 mathcalG-Adic Asymptotic Bases
2 Minimal Asymptotic Bases
3 Open Problems
References
An Inverse Problem for Finite Sidon Sets
1 Sidon Sets for Linear Forms
2 Monic Forms and Normalized Sets
3 Binary Linear Forms
4 Sidon Sets for Linear Forms in h 2 Variables
5 Open Problems
References