Books Published

With Alfred Geroldinger and Qinghai Zhong.
Combinatorial Factorization Theory: Factorization Theory in Krull Monoids via Additive Combinatorics. In progress (700+ pp.)

The Characterization of Finite Elasticities: Factorization Theory in Krull Monoid via Convex Geometry,
Lecture Notes in Mathematics 2316, Springer, 2022

Structural Additive Theory, Developments in Mathematics 30, Springer 2013

Book Reviews

MathSciNet Review MR3243507
B. Landman and A. Robertson, Ramsey theory on the integers.Second edition. Student Mathematical Library, 73. American Mathematical Society, Providence, RI, 2014. xx+384 pp.
ISBN 978-0-8218-9867-3

Refereed Journal Publications

The 3k-4 Theorem modulo a Prime: High Density for A + B. 
Submitted

with J. Ebert. Structure of a Sequence with Prescribed Zero-Sum Subsequences: Rank Two $p$-Groups.

European J. Combin. 118 (2024), Paper No. 103888, 13 pp.

A Generalization of the Chevalley-Warning and Ax-Katz Theorems with a View Towards Combinatorial Number Theory.

with Chao Liu. A Multiplicative Property for Zero-Sums II.
Electronic J. Combinatorics 29 (2022), no. 3, Paper No. 3.12, 16 pp. 

with Chao Liu.  A multiplicative property for zero-sums I.
Discrete Math. 345 (2022), no. 10, Paper No. 112974, 21 pp

with A. Geroldinger, Jun Seok Oh, and Qinghai Zhong. On Product-One Sequences over Dihedral Groups.
J. Algebra App.  21 (2022), no. 4, Paper No. 2250064, 58 pp.

with P. Candela and Gonzalez-Sanchez. On sets with small sumset and m-sum free sets in Z/pZ,
Bull. Soc. Math. France 149 (2021), no. 1, 155–177.

Representing Sequence Subsums as Sumsets of Near Equal Sized Sets.
in Combinatorial and Additive Number Theory IV, ed. M. Nathanson, Springer (2021), Ch. 11.

A Single Set Improvement to the 3k-4 Theorem.
J. Number Theory 214 (2020), 360--381.

with U. Vishne. The index of small length sequences,
International J. Algebra and Computation 30 (2020), no. 5, 977--1014.

Iterated Sumsets and Setpartitions,
Ramanujan J. 52 (2020), no. 3, 499--518.

with Chunlin Wang and Kevin Zhao. The Structure of a Sequence with Prescribed Zero-Sum Subsequences.
Integers 20 (2020) A3.

with S. Adhikari, R. Balasubramanian, and S. Eliahou, A Conjecture of Fox-Kleitman and Additive Combinatorics,
Proc. Indian Acad. Sci. Math. Sci. 129 (2019), no. 4, Art. 43.

with S. Adhikari, R. Balasubramanian, and S. Eliahou. On the degree of regularity of a particular linear equation,
Acta Arith. 184 (2018), no. 2, 187-191.

Iterated Sumsets and Subsequence Sums,
J. Combin. Theory, Ser. A, 160 (2018), 136–167.

Planar Subsets with Small Doubling.
Quart. J. Math., 68 (2017), no. 1, 161-192.

with V. Lev. Symmetric Kneser's Theorem with Trios and 3-Transform.
J. Combinatorics and Number Theory, 7 (2015), no. 3, 419–435.

with A. Geroldinger and Pingzhi Yuan. On Products of k Atoms II.
Mosc. J. Comb. Number Theory, 5 (2015), no. 3, 3-59.

with A. Chapman, E. Matrzi, L Rowen, and U. Vishne. Classification of Monomial p-
Central Spaces in Central Simple Algebras of Degree p,
Journal of Pure and Applied Algebra, 220 (2016), no. 10, 3363-3371.

with Weidong Gao and Xingwu Xia. On n-Sums in an Abelian Group.
Combinatorics, Probability and Computing, 25 (2016), no. 3, 419-435.

with F. Hennecart. A Weighted zero-sum problem with quadratic residues,
Uniform Distribution Theory, 10 (2015), no. 1, 69-105.

with D. Bernstein and C. Yerger. On three sets with nondecreasing diameter.
Discrete Math., 338 (2015), no. 8, 1328-1344.

with N. R. Baeth, A. Geroldinger, and D. Smertnig. A semigroup-theoretical view of
direct-sum decompositions and associated combinatorial problems.
Journal of Algebra and its Applications, 14 (2015), no.2, 1550016, 60 pp.

The large Davenport constant II: General Upper Bounds.
J. Pure and Applied Algebra,  217 (2013), no. 12, 2221–2246.

with P. Baginski, A. Geroldinger and A. Philipp. Products of two atoms in Krull monoids
and arithmetical characterizations of class groups.
European J. Combin., 34 (2013), no. 8, 1244–1268.

with A. Geroldinger. The large Davenport constant I: groups with a cyclic, index 2
subgroup.
J. Pure and Applied Algebra, 217 (2013), no. 5, 863-885.

with A. Philipp and V. Ponomarenko. Arithmetic progression weighted subsequence
sums.
Israel J. Math., 193 (2013), no. 1, 359-398.

with S. D. Adhikari and Z. H. Sun. On weighted zero-sum sequences.
Advances in Applied Math., 48 (2012), no. 3, 506-527.

with G. A. Freiman, O. Serra and Y. Stanchescu. Inverse additive problems for Minkowski
sumsets II.
J. Geometric Analysis, 23 (2013), no. 1, 395-414.

with G. A. Freiman, O. Serra and Y. Stanchescu. Inverse additive problems for Minkowski
sumsets I.
Collectanea Mathematica, 63 (2012), no. 3, 261-286.

Note on a conjecture of Graham.
European J. Combin., 32 (2011), no. 8, 1336-1344.

with E. Marchan and O. Ordaz. A weighted generalization of two theorems of Gao.
Ramanujan J., 28 (2012), no. 3, 323-340.

with A. Geroldinger and W. A. Schmid. The catenary degree of Krull monoids I.
J. Theor. Nombres Bordeaux, 23 (2011), no. 1, 137-169.

with A. Geroldinger and W. A. Schmid. Zero-sum problems with congruence conditions.
Acta Math. Hungar., 131 (2011), no. 4, 323-345.

with A. Geroldinger and G. J. Schaefer and W. A. Schmid. On the arithmetic of Krull
monoids with infinite cyclic class group.
Journal of Pure and Applied Algebra, 214 (2010), no. 12, 2219-2250.

with I. Bardaji. Long arithmetic progressions in sets with small sumset.
Integers, 10 (2010), 335-350, (electronic) A28.

with V. Lev. 1-saturating sets, caps, and doubling-critical sets in binary spaces.
SIAM J. Discrete Math., 24 (2010), no. 1, 169-190.

with A. Geroldinger. On the structure of minimal zero-sum sequences with maximal
cross number.
Journal of Combinatorics and Number Theory 1 (2009), no. 2, 109-126.

with A. Geroldinger. On the arithmetic of Krull monoids with finite Davenport constant.
J. Algebra, 321 (2009), 1256-1284.

On extending Pollard's Theorem for t-representable sums.
Israel J. Math., 177 (2010), no. 1, 413-439,

with W. D. Gao and A. Geroldinger. Inverse zero-sum problems III.
Acta Arithmetica, 141 (2010), 103-152.

 with E. Marchan, and O. Ordaz. Representation of finite abelian group elements by
subsequence sums.
J. Theor. Nombres Bordeaux 21 (2009), no. 3, 559-587.

with O. Serra. Properties of two dimensional sets with small sumset.
J. Combin. Theory, Ser. A, (2010), no. 2, 164-188.

with J. Zhuang. Weighted sequences in finite cyclic groups.
Applied Mathematics E-Notes, 9 (2009), 40-46.

with V. Lev, and O. Serra. Connectivity of addition Cayley graphs.
J. Combin. Theory, Ser. B, 99 (2009), 202-217.

with O. Ordaz, M. T. Varela, and F. Villarroel. On Erdos-Ginzburg-Ziv inverse theorems.
Acta Arith., 129 (2007), no. 4, 307-318.

A step beyond the Kemperman Structure Theorem.
Mathematika 55 (2009), 67-114.

On the number of m-term zero-sum subsequences.
Acta Arith., 121 (2006), no. 3, 275-298.

On a conjecture of Hamidoune for subsequence sums.
Integers, 5 (2005), no. 2, A7, 11 pp.

A weighted Erdos-Ginzburg-Ziv Theorem.
Combinatorica, 26 (2006), no. 4, 445-453.

Quasi-periodic decompositions and the Kemperman Structure Theorem.
European J. Combin., 26 (2005), no. 5, 559-575.

An extension of the Erdos-Ginzburg-Ziv Theorem to hypergraphs.
European J. Combin., 26 (2005), no. 8, 1154-1176.

with A. Bialostocki. On the intersection of two m-sets and the Erdos-Ginzburg-Ziv
Theorem.
Ars Combin. 83 (2007), 335-339.

with A. Schultz. A five color zero-sum generalization.
Graphs and Combinatorics, 22 (2006), no. 3, 351-360.

with R. Sabar. Monochromatic and zero-sum sets of nondecreasing modified diameter.
Electron. J. Combin., 13 (2006), no. 1, Research Paper 28, 19 pp.

with A. Bialostocki, P. Dierker and M. Lotspeich. On some developments of the Erdos-
Ginzburg-Ziv Theorem II.
Acta Arith., 110 (2003), no. 2, 173-184.

On four colored sets with nondecreasing diameter and the Erdos-Ginzburg-Ziv Theorem.
J. Combin. Theory Ser. A, 100 (2002), no. 1, 44-60.

On a partition analog of the Cauchy-Davenport Theorem.
Acta Math. Hungar., 107 (2005), no. 1-2, 161-174.

On four color monochromatic sets with nondecreasing diameter.
Discrete Math., 290 (2005), no. 2-3, 165-171.

On some Rado numbers for generalized arithmetic progressions.
Discrete Math., 280 (2004), no. 1-3, 39-50.

Presentations - Conference (refereed *)

New Trends in Arithmetic Combinatorics and related Fields (25w5331), 
Banff International Research Station in Granada, June 2025. 
Plenary Talk: TBA 

An Extension of the Ax-Katz Theorem Modulo Differing Prime Powers, 2022
Combinatorics Seminar, U. Mississippi

Polynomial Methods in Combinatorial Number Theory, 2022
Colloquium, U. Linz

CANT(Combinatorial and Addtive Number Theory) (Virtual), May 2021.
Characterizing infinite subsets of lattice points having finite-like behavior (30 min. talk)

Balu Fest, March 2021
Plenary Talk (60 min.): The 3k-4 Theorem Modulo a Prime for Large Density Sumsets

Joint Meetings of the AMS and MAA, Virtual, Jan. 2021.
Special Session: Finite Elasticities in Krull Domains with Finitely Generated Class Group

Workshop on Additive Combinatorics, International Center for Theoretical Sciences (ICTS-TIFR), Bangalore, Feb. 2020 - Mar 2020.
Plenary Talk Series (5 Lectures): Set Addition

Zero-Sum Ramsey Theory: Graphs, Sequences and More (19w5132), CMO Banff International Research Station, Oaxaca, Nov. 2019.
Plenary Talk: Sequence Subsums in Zero-Sum Theory

Joint International Meeting of the CMS and AMS, Shanghai, June 2018
Special Session Organizer: Additive Combinatorics and its Interplay with Factorization Theory

Conference on Rings and Factorizations, Graz, Feb. 2018
Plenary Talk: Finiteness of the  Elasticities  $rho_k(G_0)$ Inside a Lattice

Combinatorial and Additive Number Theory, Graz, Jan. 2016
Plenary Talk: The Freiman 3k-4 Theorem

Additive Combinatorics in Marseille, Marseille, Sep. 2015.
Short Plenary Talk: Symmetric Kneser's Theorem with Trios and 3-Transform

Joint Meeting of the AMS and MAA, 2015
(AMS) Special Session: On Sets of Lengths in Krull Monoids.

The Index of Zero-Sum Free Sequences and Kummer Subspaces.
University of Graz, Austria, 2014.

Joint Meeting of the Israel Mathematical Union and the AMS, 2014
Special Session in Additive Number Theory: The Index of Minimal Zero-Sum Sequences
and Kummer Subspaces.

Joint Meetings of the AMS and MAA, 2013
(AMS) Special Session: The large Davenport constant for Non-abelian groups

Joint Meetings of the AMS and MAA, 2013
(AMS) Special Session: The large Davenport constant for Non-abelian groups

Additive Combinatorics in Paris, July 2012
Short Plenary Talk: Sidon sets and the isoperimetric method

Wilsonfest, Caltech, March 2012
Plenary Speaker: Freiman homomorphisms

DocCourse in Additive Combinatorics, CRM, Barcelona, Feb. 2008.
Problem Session Course (jointly taught with W. Schmid): Additive group theory and the
theory of non-unique factorization

Presentations - Universities/Industry (refereed *)

TU Graz, School of Discrete Mathematics, Austria, 2024    
Seminar: Inverse Sumset Results mod p at High Density

Inverse Question for the Davenport Constant in Rank Two Groups (2 parts), 2023.
Guest Lecturer for Doctoral Student Course, University of Graz.

Subsequence Sums: Optimal Bounds in the Partition Theorem and the Gao-Olson Generalization of the EGZ Theorem.
Nankai University, Center for Combinatorics, 2018

On the Degree of Regularity of (x_1-y_1)+...+(x_1-y_k)=c
University of Graz, 2017

A Zero-Sum Conjecture of Hamidoune
U. Mississippi, 2016

The  rho_k Invariants for Finite Abelian Groups
University of Graz, Austria, 2015

Some Topics in Additive Theory
Heriot-Watt University, Edinburgh, 2013

Additive Theory
University College Dublin, 2013

On a Weighted Generalization of Two Theorems of Gao VI, 2010.
Harisch Chandra Research Institute, India.

On a Weighted Generalization of Two Theorems of Gao V, 2010.
Harisch Chandra Research Institute, India.

On a Weighted Generalization of Two Theorems of Gao IV, 2010.
Harisch Chandra Research Institute, India.

On a Weighted Generalization of Two Theorems of Gao III, 2010.
Harisch Chandra Research Institute, India.

On a Weighted Generalization of Two Theorems of Gao II, 2010.
Harisch Chandra Research Institute, India.

On a Weighted Generalization of Two Theorems of Gao I, 2010.
Harisch Chandra Research Institute, India.

Sumset bounds for two-dimensional sets.
U. Deleware, 2008.

Extremal examples for the Davenport constant in rank two groups.
Technical University of Catalunya (UPC), Barcelona, 2008.

On the multiplicity of zero-sum subsequences.
U. Paris VI, 2006.

Other Presentations (refereed *)

Conference on Rings and Factorizations 2023, University of Graz, Austria, 2023.
Parallel Session: Zero-Sums in $p$-groups via a Generalization of the Ax-Katz Theorem.

A Chevalley Warning Theorem Modulo Differing Prime Powers (2 parts), 2022
Combinarics Seminar, U. Memphis

CANT 2019, CUNY, New York, May 2019.
Main Session: An Inverse Zero-Sum Problem for Elementary Abelian p-groups of rank two.

6th Annual Mississippi Discrete Math Workshop, U. Mississippi, 2018.
Parallel Session: Improving Olson's Generalization of the Erdos-Ginzburg-Ziv Theorem

Integers Conference, Augusta GA, 2018
Parallel Session: Exact Bounds in the Gao-Olson Complete Sequence Theorem

Discrete Mathematics Days, Sevilla, 2018
Parallel Session: Iterated Sumsets and Olson's Generalization of the Erdos-Ginzburg-Ziv Theorem

The Freiman 3k-4 Theorem
University of Memphis, 2016

Zero-Sums and Polynomial
University of Memphis, 2016

Sumsets and t-Popular Sums
University of Memphis

Journees Arithmetiques, Debrecen, July 2015.
Parallel Session: Pairwise Balanced Designs and Weighted Davenport Constants.

Sumsets and Homomorphisms
University of Memphis, 2013

Integers Conference, U. West Georgia, October 2011
Parallel Session: Freiman homomorphisms

Journees Arithmetiques, Vilnius, June 2011
Parallel Session: On Freiman's 3k - 4 Theorem in groups of prime order

OMG + DMV Kongress, Graz 2009
Parallel Session: On Pollard's Theorem for general abelian groups

Journees Arithmetiques, St. Etienne, July 2009.
Parallel Session: The catenary degree of Krull monoids.

Eurocomb 2007, Sevilla, Sep. 2007.
Parallel Session: The connectivity of addition Cayley graphs.

Joint Meeting of the AMS and MAA, New Orleans, Jan. 2007.
Parallel Session: Extending the Freiman 3k - 3 Theorem to distinct sets.

2nd Meeting of the Czech and Catalan Mathematical Societies, Barcelona, Sep. 2006.
Parallel Session: On two zero-sum conjectures of Gao, Thangadurai and Zhuan.

Rencontres Arithmetique et Combinatoire, St. Etienne, France, 2006.
Parallel Session: The structure of subsets of an arbitrary abelian group with a small
sumset |A + B| = |A| + |B|.

AMS Sectional Meeting, Santa Barbara, 2006.
Parallel Session: A weighted version of the Erdos-Ginzburg-Ziv Theorem.

CANT 2005, New York.
Parallel Session: The Erdos-Ginzburg-Ziv Theorem in hypergraphs.

Integers Conference, U. West Georgia, Oct./Nov. 2003.
Contributed Paper: On a conjecture of Hamidoune for subsequence sums

Joint Meeting of the AMS and MAA, New Orleans, Jan. 2001.
Parallel Session: On a conjecture of Bialostocki, Erdos, and Lefmann.

MAA Fall Northeastern Section Meeting, Providence, Rhode Island, 2000.
Student Session: On a conjecture of Bialostocki, Erdos, and Lefmann.       

Appendix A

Appendix B

Appendix D

Appendix E