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.
Inverse zero-sum problems III
With W. D. Gao and A. Geroldinger
Acta Arithmetica
141 (2010), 103--152.
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.
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.
Long Arithmetic Progressions in Sets with Small Sumset
With I. Bardaji.
10 (2010), 335--350, (electronic) A28.
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.
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 Arithmetica,
To appear. pdf

On a Conjecture of Fox-Kleitman and Additive Combinatorics
with S. Adhikari, R. Balasubramanian, and S. Eliahou
Submitted. pdf
Iterated Sumsets and Setpartitions Submitted. pdf
The Index of Small Length Sequences
with Uzi Vishne
Submitted. 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

To appear. Pdf


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

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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: 27.08.2018