| 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 149 (2021), no. 1, 155–177. pdf |
| On Product-One
Sequences over Dihedral Groups With A. Geroldinger, Jun Seok Oh, and Qinghai Zhong |
J. Algebra
App. 21 (2022), no. 4, Paper No. 2250064, 58 pp. pdf |
| A multiplicative property for
zero-sums I With Chao Liu |
Discrete Math. 345 (2022), no. 10, Paper No. 112974, 21 pp. pdf |
| A multiplicative
property for zero-sums II With Chao Liu |
Electron. J. Combin. 29 (2022), no. 3, Paper No. 3.12, 16 pp. pdf |
| A Generalization of the
Chevalley-Warning and Ax-Katz Theorems with a View Towards
Combinatorial Number Theory. |
to appear in Combinatorica
(pending approval of minor revisions). pdf |
| Structure of a Sequence with
Prescribed Zero-Sum Subsequences: Rank Two p-Groups. With J. Ebert |
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 |
Combinatorica
39 (2019), 1281–1315. Pdf |
| Structural Additive Theory |
Developments
in Mathematics 30 (2013), Springer, xii+426 pp. Table of Contents Springer Link |
| The
Characterization of Finite Elasticities: Factorization Theory in Krull Monoids via Convex Geometry |
Lecture Notes
in Mathematics 2316, (2022) Springer, 280 pp. pdf |
