Landman Integers

Annual Volume 2013
1. Auflage 2014
ISBN: 978-3-11-029816-1
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 1091 Seiten

"Integers" is a refereed online journal devoted to research in the area of combinatorial number theory. It publishes original research articles in combinatorics and number theory. Topics covered by the journal include additive number theory, multiplicative number theory, sequences and sets, extremal combinatorics, Ramsey theory, elementary number theory, classical combinatorial problems, hypergraphs, and probabilistic number theory. Integers also houses a combinatorial games section.This work presents all papers of the 2013 volume in book form.

Zielgruppe

Mathematicians working in combinatorics and number theory; librar

Autoren/Hrsg.

Landman, Bruce

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

1;PREFACE TO VOLUME 13 OF INTEGERS;5
2;CONTENTS;7
3;SIMPLE ARITHMETICAL CRITERIA FOR IRREDUCIBILITY OF POLYNOMIALS WITH INTEGER COEFFICIENTS;13
4;A SHORT PROOF OF A RESULT OF GICA AND LUCA;34
5;COUNTING HERON TRIANGLES WITH CONSTRAINTS;36
6;RAMSEY TYPE RESULTS ON THE SOLVABILITY OF CERTAIN EQUATIONS IN ZM;53
7;A COMBINATORIAL PROOF OF S-ADICITY FOR SEQUENCES WITH LINEAR COMPLEXITY;62
8;ON INTERPOLATING POWER SERIES;81
9;CAPTURED-REVERSIBLE MOVES AND STAR DECOMPOSITION DOMINATION IN HEX;87
10;ON BOUNDS FOR TWO DAVENPORT-TYPE CONSTANTS;101
11;ON THE DIOPHANTINE EQUATION x² - kxy + y² + lx = 0;104
12;ON A SEQUENCE OF POLYNOMIALS WITH HYPOTHETICALLY INTEGER COEFFICIENTS;112
13;ON DIVISIBILITY PROPERTIES OF SOME DIFFERENCES OF THE CENTRAL BINOMIAL COEFFICIENTS AND CATALAN NUMBERS;141
14;GENERALIZED BINOMIAL EXPANSIONS AND BERNOULLI POLYNOMIALS;161
15;THE DISTRIBUTION OF SOLUTIONS TO xy = n (mod a) WITH AN APPLICATION TO FACTORING INTEGERS;174
16;DISTRIBUTION LAWS OF PAIRS OF DIVISORS;194
17;SHARP THRESHOLD ASYMPTOTICS FOR THE EMERGENCE OF ADDITIVE BASES;207
18;ON AN ANALOGUE TO THE LUCAS-LEHMER-RIESEL TEST USING ELLIPTIC CURVES;224
19;RESTRICTED INTEGER PARTITION FUNCTIONS;240
20;BRUN MEETS SELMER;249
21;THICK SUBSETS THAT DO NOT CONTAIN ARITHMETIC PROGRESSIONS;261
22;COFINITE INDUCED SUBGRAPHS OF IMPARTIAL COMBINATORIAL GAMES: AN ANALYSIS OF CIS-NIM;271
23;PIRATES AND TREASURE;298
24;TAKING THE CONVOLUTED OUT OF BERNOULLI CONVOLUTIONS: A DISCRETE APPROACH;316
25;SOME RESULTS ON BALANCING, COBALANCING, (a, b)-TYPE BALANCING, AND (a, b)-TYPE COBALANCING NUMBERS;328
26;VALUATIONS AND COMBINATORICS OF TRUNCATED EXPONENTIAL SUMS;342
27;STRICT SCHUR NUMBERS;358
28;ON q-ANALOG OF WOLSTENHOLME TYPE CONGRUENCES FOR MULTIPLE HARMONIC SUMS;370
29;ON THE FOURIER TRANSFORM OF THE GREATEST COMMON DIVISOR;381
30;WEIGHTED LONESUM MATRICES AND THEIR GENERATING FUNCTION;397
31;ON MULTIPLICATIVE SIDON SETS;404
32;SOME WEIGHTED SUMS OF PRODUCTS OF LUCAS SEQUENCES;414
33;ADDITIVE ENERGY AND THE FALCONER DISTANCE PROBLEM IN FINITE FIELDS;423
34;A COMBINATORIAL INTERPRETATION OF THE CATALAN AND BELL NUMBER DIFFERENCE TABLES;433
35;PISOT NUMBERS AND CHROMATIC ZEROS;452
36;COORDINATE SUM AND DIFFERENCE SETS OF d-DIMENSIONAL MODULAR HYPERBOLAS;459
37;AN INFINITE FAMILY OF RECURSIVE FORMULAS GENERATING POWER MOMENTS OF KLOOSTERMAN SUMS WITH TRACE ONE ARGUMENTS: O(2n + 1, 2r) CASE;475
38;THE DIOPHANTINE EQUATION Fyn + Fxn+1 = Fxm;491
39;A NOTE ON THE MULTIPLICATIVE STRUCTURE OF AN ADDITIVELY SHIFTED PRODUCT SET AA + 1;508
40;REPRESENTATIONS OF SQUARES BY CERTAIN SEPTENARY QUADRATIC FORMS;516
41;CATALAN NUMBERS MODULO A PRIME POWER;534
42;GONI: PRIMES REPRESENTED BY BINARY QUADRATIC FORMS;538
43;A COMBINATORIAL PROOF OF TWO EQUIVALENT IDENTITIES BY FREE 2-MOTZKIN PATHS;556
44;IMPROVING THE CHEN AND CHEN RESULT FOR ODD PERFECT NUMBERS;564
45;FINITE SUMS THAT INVOLVE RECIPROCALS OF PRODUCTS OF GENERALIZED FIBONACCI NUMBERS;572
46;COMPOSITIONS CONSTRAINED BY GRAPH LAPLACIAN MINORS;583
47;EDGE GROWTH IN GRAPH SQUARES;605
48;NEW BOUNDS AND COMPUTATIONS ON PRIME-INDEXED PRIMES;625
49;GAP DISTRIBUTION OF FAREY FRACTIONS UNDER SOME DIVISIBILITY CONSTRAINTS;646
50;ONE FINITE SUMS AND INTEGRAL REPRESENTATIONS;661
51;FINE-WILF GRAPHS AND THE GENERALIZED FINE-WILF THEOREM;673
52;ON THE LEAST SIGNIFICANT 2-ADIC AND TERNARY DIGITS OF CERTAIN STIRLING NUMBERS;691
53;ON THE DENSITY OF HAPPY NUMBERS;701
54;A REMARK ON RELATIVELY PRIME SETS;726
55;INTERSECTING RATIONAL BEATTY SEQUENCES;740
56;NEW PROOFS FOR THE p, q-ANALOGUE OF CHU-VANDERMONDE’S IDENTITY;753
57;REMARKS ON TINY ZERO-SUM SEQUENCES;764
58;A NOTE ON IRREGULARITIES OF DISTRIBUTION;772
59;GENERALIZING DELANNOY NUMBERS VIA COUNTING WEIGHTED LATTICE PATHS;776
60;ON THE LEAST PRIMITIVE ROOT EXPRESSIBLE AS A SUM OF TWO SQUARES;809
61;STABILIZATION OF COEFFICIENTS FOR PARTITION POLYNOMIALS;816
62;ON SETS WITH MORE RESTRICTED SUMS THAN DIFFERENCES;831
63;ON AN INCOMPLETE ARGUMENT OF ERDO S ON THE IRRATIONALITY OF LAMBERT SERIES;855
64;GENERALIZATION OF UNIVERSAL PARTITION AND BIPARTITION THEOREMS;861
65;SOME WEIGHTED SUMS OF POWERS OF FIBONACCI POLYNOMIALS;872
66;CONGRUENCES OF CONCAVE COMPOSITION FUNCTIONS;891
67;DISJUNCTIVE RADO NUMBERS FOR ax1 + x2 = x3 AND bx1 + x2 = x3
;898
68;HOW TO WRITE A PERMUTATION AS A PRODUCT OF INVOLUTIONS (AND WHY YOU MIGHT CARE);909
69;ON THE HIGHER-DIMENSIONAL GENERALIZATION OF A PROBLEM OF ROTH;929
70;INDEPENDENT DIVISIBILITY PAIRS ON THE SET OF INTEGERS FROM 1 TO N;936
71;CYCLES IN REPEATED EXPONENTIATION MODULO pn;949
72;COMPUTATION OF AN IMPROVED LOWER BOUND TO GIUGA’S PRIMALITY CONJECTURE;956
73;CONVOLUTION SUMS INVOLVING LEGENDRE-JACOBI SYMBOL AND DIVISOR FUNCTIONS;970
74;OPTIMAL PRIMITIVE SETS WITH RESTRICTED PRIMES;984
75;A ZERO-SUM THEOREM OVER Z;994
76;ON THE DIVISIBILITY OF an ± bn BY POWERS OF n;1005
77;LOWER BOUNDS FOR SUMSETS OF MULTISETS IN Z2p
;1011
78;ON SEQUENCES WITHOUT GEOMETRIC PROGRESSIONS;1028
79;INCLUSION-EXCLUSION POLYNOMIALS WITH LARGE COEFFICIENTS;1033
80;AN EXPLICIT FORMULA FOR HIGHER ORDER BERNOULLI POLYNOMIALS OF THE SECOND KIND;1036
81;A NOTE ON A CONJECTURE OF ERDO
S, GRAHAM, AND SPENCER;1043
82;SQUARES AND DIFFERENCE SETS IN FINITE FIELDS;1049
83;A FAMILY OF FIBONACCI-LIKE CONDITIONAL SEQUENCES;1054
84;ON THE RESIDUE CLASSES OF p
(n) MODULO t;1068
85;S-DIOPHANTINE QUADRUPLES WITH TWO PRIMES CONGRUENT TO 3 MODULO 4;1078
86;THE AVERAGE LARGEST PRIME FACTOR;1087

Über Autor(innen)

Melvyn B. Nathanson, CUNY, New York, USA
Jaroslav Nešetril, Charles University, Prague, Czech Republic
Carl Pomerance, Dartmouth College, Hanover, NH, USA.
Richard J. Nowakowski, Dalhousie University, Halifax, Canada
Bruce Landman, University of West Georgia, Georgia, USA
Aaron Robertson, Colgate University, New York, USA