Combinatorial and additive number theory V : CANT, New York, USA 2021 / / edited by Melvyn B. Nathanson

• Record Nr.: UNISA996503549903316
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 9783031107962; 9783031107955
• Descrizione fisica: 1 online resource (290 pages)
• Collana: Springer Proceedings in Mathematics and Statistics ; ; v.395
• Disciplina: 069
• Soggetti: Algebra; Teoria de nombres; Congressos; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- 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) &gt -- 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&lt -- θ&lt -- 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.