LEADER 06330nam 2200505 450 001 996503549903316 005 20231110221116.0 010 $a9783031107962$b(electronic bk.) 010 $z9783031107955 035 $a(MiAaPQ)EBC7166112 035 $a(Au-PeEL)EBL7166112 035 $a(CKB)25913695500041 035 $a(PPN)267814437 035 $a(EXLCZ)9925913695500041 100 $a20230505d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aCombinatorial and additive number theory V $eCANT, New York, USA 2021 /$fedited by Melvyn B. Nathanson 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (290 pages) 225 1 $aSpringer Proceedings in Mathematics and Statistics ;$vv.395 311 08$aPrint version: Nathanson, Melvyn B. Combinatorial and Additive Number Theory V Cham : Springer International Publishing AG,c2023 9783031107955 320 $aIncludes bibliographical references. 327 $aIntro -- 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 ?. 327 $a5 The Intertwining Operator ? -- 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 `3?9`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 ?(r)z=1, ?(r)z=1 and ?(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(B?) -- 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< -- ?< -- ? -- 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. 327 $a3 Graphs, Operators and Eigenvalues -- 4 Main Part of the Proof: Counting Closed Walks -- 5 Conclusions -- References -- Sums of Squares: Methods for Proving Identity Families -- 1 Motivation -- 2 Examples -- 3 Main Theorem: Statement and Proof Outline -- 4 The Seven Coefficient Groups -- 5 Detailed Outline of Proof -- 6 The Five Summands -- 7 Index Tables for Summand-I Through Summand-V -- 8 Distribution of Ni,j Across Index Sets -- 9 Conclusion -- References -- Generalized Bernoulli Numbers, Cotangent Power Sums, and Higher-Order Arctangent Numbers -- 1 Introduction -- 2 Proofs -- References -- A New Class of Minimal Asymptotic Bases -- 1 mathcalG-Adic Asymptotic Bases -- 2 Minimal Asymptotic Bases -- 3 Open Problems -- References -- An Inverse Problem for Finite Sidon Sets -- 1 Sidon Sets for Linear Forms -- 2 Monic Forms and Normalized Sets -- 3 Binary Linear Forms -- 4 Sidon Sets for Linear Forms in h 2 Variables -- 5 Open Problems -- References. 410 0$aSpringer Proceedings in Mathematics and Statistics 606 $aAlgebra 606 $aTeoria de nombres$2thub 608 $aCongressos$2thub 608 $aLlibres electrònics$2thub 615 0$aAlgebra. 615 7$aTeoria de nombres 676 $a069 702 $aNathanson$b Melvyn B. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a996503549903316 996 $aCombinatorial and additive number theory V$93363631 997 $aUNISA