Publications of David J. Grynkiewicz



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Sumsets, Zero-Sums and Extremal Combinatorics
Ph.D. Dissertation, Caltech
2005 pdf
On some Rado numbers for generalized arithmetic progressions Discrete Math.
280 (2004),  no. 1-3, 39--50. pdf
On four color monochromatic sets with nondecreasing diameter Discrete Math.
290  (2005), no. 2-3, 165--171. pdf
On a partition analog of the Cauchy-Davenport theorem Acta Math. Hungar.
107  (2005), no. 1-2, 161--174. pdf
On four colored sets with nondecreasing diameter and the Erdös-Ginzburg-Ziv Theorem J. Combin. Theory Ser. A
100 (2002),  no. 1, 44--60.
On some developments of the Erdös-Ginzburg-Ziv theorem II
    with A. Bialostocki, P. Dierker and M. Lotspeich
Acta Arith.
110  (2003),  no. 2, 173--184. pdf
Monochromatic and zero-sum sets of nondecreasing modified diameter
     with R. Sabar
Electron. J. Combin.
13  (2006),  no. 1, Research Paper 28, 19 pp. pdf
A Five Color Zero-Sum Generalization
     with A. Schultz.
Graphs and Combinatorics
22 (2006), no. 3, 351--360. pdf
On the Intersection of two m-sets and the Erdös-Ginzburg-Ziv theorem
     with A. BialostockI
Ars Combin.
83  (2007), 335--339. pdf
An extension of the Erdös-Ginzburg-Ziv theorem to hypergraphs European J. Combin.
26 (2005),  no. 8, 1154--1176. pdf
Quasi-periodic decompositions and the Kemperman structure theorem European J. Combin.
26 (2005), no. 5, 559--575. pdf
A weighted Erdös-Ginzburg-Ziv theorem Combinatorica
26 (2006), no. 4, 445--453. pdf
On a conjecture of Hamidoune for subsequence sums Integers
5  (2005),  no. 2, A7, 11 pp. pdf
On the number of m-term zero-sum subsequences Acta Arith.
121  (2006), no. 3, 275--298. pdf
A Step Beyond the Kemperman Structure Theorem Mathematika
55 (2009), 67--114 pdf
On Erdös-Ginzburg-Ziv Inverse Theorems
     with O. Ordaz, M. T. Varela, and F.Villarroel
Acta Arith.
129  (2007),  no. 4, 307--318. pdf
Connectivity of addition Cayley graphs
     With V. Lev, and O. Serra
J. Combin. Theory, Ser. B
99 (2009), 202--217. pdf
Weighted Sequences in Finite Cyclic Groups
     with J. Zhuang
Applied Mathematics E-Notes
9 (2009), 40--46. pdf
Representation of finite abelian group elements by subsequence sums
     with E. Marchan and O. Ordaz.
J. Théor. Nombres Bordeaux
21 (2009), no. 3,  559--587. pdf
Properties of Two Dimensional Sets with Small Sumset
     with O. Serra
J. Combin. Theory, Ser. A
(2010), no. 2, 164--188. pdf
Inverse zero-sum problems III
     with W. D. Gao and A. Geroldinger
Acta Arithmetica
141 (2010), 103--152. pdf
On Extending Pollard's Theorem for t-Representable Sums Israel J. Math
177 (2010), no. 1, 413--439. pdf
On the arithmetic of Krull monoids  with finite Davenport constant
     with A. Geroldinger
J. Algebra.
321 (2009), 1256--1284. pdf
On the structure of minimal zero-sum sequences with maximal cross number
     with A. Geroldinger
J. Combin. and Number Theory
1 (2010), no. 2, 109--126. pdf
1-Saturating sets, caps, and doubling-critical sets in binary spaces
     with V. Lev.
SIAM J. Discrete Math
24 (2010), no. 1, 169--190. pdf
Long Arithmetic Progressions in Sets with Small Sumset
     with I. Bardaji.
Integers
10 (2010), 335--350, (electronic) A28. pdf
Note on a Conjecture of Graham European J. Combin.
32 (2011), no. 8,  1336-1344. pdf
A Weighted Generalization of Two Conjectures of Gao
     with O. Ordaz and E. Marchan.
Ramanujan J.
28 (2012),  no. 3, 323-340. pdf
On the arithmetic of Krull monoids with infinite cyclic class group
     with A. Geroldinger, G. J. Schaeffer,  and W. A. Schmid
J. Pure and Appl. Alg.
 214 (2010), no. 12, 2219--2250. pdf
Zero-sum problems with congruence conditions
    with A. Geroldinger and W. A. Schmid
Acta Math. Hungar.
131 (2011), 323-345. pdf
The catenary degree of Krull monoids I
     wtih A. Geroldinger and W. A. Schmid
J. Théor. Nombres Bordx.
23 (2011), 137-169.
pdf
Inverse Additive Problems for Minkowski Sumsets I
     with G. A. Freiman, O. Serra and Y. Stanchescu
Collectanea Math.
63 (2012), no. 3, 261-286. pdf
Inverse Additive Problems for Minkowski Sumsets II
    
with G. A. Freiman, O. Serra and Y. Stanchescu
J. Geom. Anal.
23 (2013), no. 1, 395-414. pdf
On Weighted Zero-sum Sequences
     with S. Adhikari and Z. W. Sun
Adv. Apl. Math.
48 (2012), 506-526. pdf
Arithmetic Progression Weighted Subsequence Sums
     with A. Philipp and V. Ponomarenko
Israel J. Math.
191 (2013), no. 1, 359-398. pdf
Products of Two Atoms in Krull Monoids and Arithmetical Characterization of Class Groups
     with P. Baginski, A. Geroldinger and A. Philipp
European J. Combin.
34 (2013), no. 8, 1244-1268. pdf
The Large Davenport Constant I: Groups with a Cyclic, Index 2 Subgroup
     with Alfred Geroldinger
J. Pure and Applied Alg.
217 (2013), no. 5, 863-885. pdf
The Large Davenport Constant II: General Upper Bounds J. Pure and Applied Alg.
217 (2013), no. 12, 2221-2246. pdf
A semigroup-theoretical view of direct-sum decompositions and associated combinatorial problems
     with N. Baeth, A. Geroldinger, and D. Smertnig
J. Algebra Appl.
14 (2015), no.2, 1550016, 60 pp. pdf
On Three Sets with Nondecreasing Diameter
     with D. Bernstein and C. Yerger
Discrete Math.
338 (2015), no. 8, 1328-1344. pdf
A Weighted Zero-Sum Problem with Quadratic Residues
     with F. Hennecart
Uniform Distribution Theory
10 (2015), no. 1., 69-105. pdf
On n-Sums in an Abelian Group
     with Weidong Gao and Xingwu Xia
Combinatorics, Probability and Computing
25 (2016), no. 3,  419-435. pdf
Kummer Spaces in Cyclic Algebras of Prime Degree
     with A. Chapman, E. Matzri, L. Rowen and U. Vishne
J. Pure Appl. Algebra
220 (2016), no. 10, 3363-3371. pdf
On Products of k Atoms II
     with A. Geroldinger and Pingzhi Yuan
Mosc. J. Comb. Number Theory
5 (2015), no. 3, 3-59. pdf
Symmetric Kneser's Theorem with Trios and 3-Transform
     with V. Lev
J. Combin. and Number Theory
7 (2015), no. 3, 191–212. pdf
Planar Subsets with Small Doubling
Quart. J. Math
68 (2017), no. 1, 161–-192. pdf
Iterated Sumsets and Subsequence Sums
J. Combin. Theory, Ser. A
160 (2018), 136-167. pdf
On the degree of regularity of a particular linear equation
     with S. Adhikari, R. Balasubramanian, and S. Eliahou
Acta Arith.1
84 (2018), no. 2, 187–191. pdf
On a Conjecture of Fox-Kleitman and Additive Combinatorics
     with S. Adhikari, R. Balasubramanian, and S. Eliahou
Proc. Indian Acad. Sci. Math. Sci.
129 (2019), no. 4, Art. 43. pdf
Iterated Sumsets and Setpartitions Ramanujan J.
52 (2020), no. 3, 499-518. pdf
The Index of Small Length Sequences
     With Uzi Vishne
International J. Algebra and Computation
30 (2020), no. 5, 977-1014. pdf
The Structure of a Sequence with Prescribed Zero-Sum Subsequences
    With Chunlin Wang and Kevin Zhao
Integers
20 (2020) A3. pdf
A Single Set Improvement to the 3k-4 Theorem J. Number Theory
214 (2020), 360-381. pdf
Representing Sequence Subsums as Sumsets of Near Equal Sized Sets
in Combinatorial Number Theory IV.
ed. M. Nathanson, Springer (2021), Ch. 11. pdf
On Sets with Small Sumset and m-sum-free sets in Z/pZ
    With P. Candela and D. González-Sánchez
Bull. Soc. Math. France
To Appear. pdf
On Product-One Sequences over Dihedral Groups
    With A. Geroldinger, Jun Seok Oh, and Qinghai Zhong
J. Algebra App.
To Appear. pdf

Hyper-Atoms Applied to the Critical Pair Theory
Yahya O. Hamidioune

Note: Yahya passed away before completing revisions to an already submitted manuscript, which I was later asked to complete.
The research in this paper is Yahya's except where otherwise noted. RIP

Combinatorica
39 (2019),
12811315. Pdf


                    Monographs

Structural Additive Theory
Developments in Mathematics 30
(2013), Springer, xii+426 pp
.
      
Table of Contents
Springer Link

The Characterization of Finite Elasticities
233 pp. Submitted December 2020. pdf


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Disclaimer: All files of manuscripts are my personal copies and may differ from later published forms, particularly with some of the older articles and with those not yet accepted.

Last Updated: 09.02.2021