This page lists my publications and will be updated with corrigenda as needed. I would be grateful to readers who inform me of any errors they may find, so that appropriate corrections can be made available.

Preprints

  1. Power Semigroups and Two Rigidity Theorems for Groups
    with S. Liu (under review · arXiv:2606.01917)
  2. The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties
    with F. Campanini and L. Cossu (under review · arXiv:2502.06610)
  3. On global isomorphisms and a closure property of semigroups
    with L. Li (under review · arXiv:2510.00772)
  4. The Automorphism Group of the Finitary Power Monoid of the Integers under Addition
    with K. Wen (under review · arXiv:2504.12566)

Publications

  1. On the automorphisms of the power semigroups of numerical semigroups
    Trans. London Math. Soc. 13 (2026), No. 1 (with K. Wen)
    DOI · arXiv
  2. Power monoids and their arithmetic: a survey
    Amer. Math. Monthly, to appear
    DOI (coming soon) · arXiv:2602.15754)
  3. A stronger Mirsky–Newman theorem
    Amer. Math. Monthly, to appear
    DOI (coming soon) · arXiv (coming soon)
  4. Torsion groups and the Bienvenu–Geroldinger conjecture
    Bull. London Math. Soc., to appear (with W. Yan)
    DOI (coming soon) · arXiv:2503.08615
  5. On the Ingham–Jessen Inequality for Measure Spaces
    Results in Math. 80 (2025), Art. No. 219, 13 pp. (with D. Głazowska, P. Leonetti & J. Matkowski)
    DOI · arXiv:2305.03227
  6. On the arithmetic of power monoids
    J. Algebra 686 (2026), 793–813 (with L. Cossu)
    DOI · arXiv:2503.08615
  7. Semigroups of ideals and isomorphism problems
    Proc. Amer. Math. Soc. 153 (2025), 2323–2339 (with P. A. García-Sánchez)
    DOI · arXiv:2410.15622
  8. On power monoids and their automorphisms
    J. Combinatorial Theory, Ser. A 209 (2025), Art. 105961, 16 pp. (with W. Yan)
    DOI · arXiv:2312.04439
  9. On the finiteness of certain factorization invariants
    Arkiv för Matematik 62 (2024), 21–38 (with L. Cossu)
    DOI · arXiv:2301.09961
  10. A conjecture by Bienvenu and Geroldinger on power monoids
    Proc. Amer. Math. Soc. 153 (2025), 913–919 (with W. Yan)
    DOI · arXiv:2310.17713
  11. On the density of sumsets, II
    Bull. Australian Math. Soc. 109 (2024), 414–419 (with L. Cossu)
    DOI · arXiv:2212.11176
  12. On the isomorphism problem for power semigroups
    In: M. Brešar, A. Geroldinger, B. Olberding, D. Smertnig (eds.),
    Recent Progress in Ring and Factorization Theory,
    Springer Proc. Math. Stat. 477, Springer, 2024, pp. 429–437
    DOI · arXiv:2402.11475
  13. Factorization under Local Finiteness Conditions
    J. Algebra 630 (2023), 128–161 (with L. Cossu)
    DOI · arXiv:2208.05869
  14. A characterisation of atomicity
    Math. Proc. Cambridge Phil. Soc. 175 (2023), 459–465
    DOI · arXiv:2209.05238
  15. Abstract Factorization Theorems with Applications to Idempotent Factorizations
    Israel J. Math. 263 (2024), 349–395 (with L. Cossu)
    DOI · arXiv:2108.12379
  16. An Abstract Factorization Theorem and Some Applications
    J. Algebra 602 (2022), 352–380
    DOI · arXiv:2102.01598
  17. On the density of sumsets
    Monatshefte für Mathematik 198 (2022), 565–580 (with P. Leonetti)
    DOI · arXiv:2001.10413
  18. On Small Sets of Integers
    Ramanujan Journal 57 (2022), 275–289 (with P. Leonetti)
    DOI · arXiv:1905.08075
  19. On strongly primary monoids, with a focus on Puiseux monoids
    J. Algebra 567 (2021), 310–345 (with A. Geroldinger & F. Gotti)
    DOI · arXiv:1910.10270
  20. On half-factoriality of transfer Krull monoids
    Communications in Algebra 49 (2021), 409–420 (with W. Gao, C. Liu, & Q. Zhong)
    DOI · arXiv:1911.04267
  21. On the Arithmetic of Power Monoids and Sumsets in Cyclic Groups
    Pacific J. Math. 312 (2021), 279–308 (with A. A. Antoniou)
    DOI · arXiv:1804.10913
  22. On the notions of upper and lower density
    Proc. Edinburgh Math. Soc. 63 (2020), 139–167 (with P. Leonetti)
    DOI · arXiv:1506.04664
  23. Structural properties of subadditive families with applications to factorization theory
    Israel J. Math. 234 (2019), 1–35
    DOI · arXiv:1706.03525
  24. Generalized Goncarov polynomials (with R. Lorentz and C. H. Yan)
    In: S. Butler, J. Cooper, and G. Hurlbert (eds.),
    Connections in Discrete Mathematics. A Celebration of the Work of Ron Graham,
    Cambridge Univ. Press, 2018, pp. 56–85
    DOI · arXiv:1511.04039
  25. Power monoids: A bridge between factorization theory and arithmetic combinatorics
    J. Algebra 512 (2018), 252–294 (with Y. Fan)
    DOI · arXiv:1701.09152
  26. On the number of distinct prime factors of a sum of superpowers
    J. Number Theory 186 (2018), 226–237 (with P. Leonetti)
    DOI · arXiv:1511.08784
  27. Commutativity of integral quasi-arithmetic means on measure spaces
    Acta Mathematica Hungarica 153 (2017), 350–355 (with D. Głazowska, P. Leonetti & J. Matkowski)
    DOI · arXiv:1703.03938
  28. Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules
    J. Algebra Appl. 16 (2017), Art. 1750234, 42 pp. (with Y. Fan, A. Geroldinger & F. Kainrath)
    DOI · arXiv:1612.03116
  29. Upper and lower densities have the strong Darboux property
    J. Number Theory 174 (2017), 445–455 (with P. Leonetti)
    DOI · arXiv:1510.07473
  30. Multivariate Delta Gončarov and Abel Polynomials
    J. Math. Analysis Appl. 446 (2017), 663–680 (with R. Lorentz & C. H. Yan)
    DOI · arXiv:1608.05836
  31. On the commutation of generalized means on probability spaces
    Indagationes Mathematicae 27 (2016), 945–953 (with P. Leonetti & J. Matkowski)
    DOI · arXiv:1503.01139
  32. Sums of Dilates in Ordered Groups
    Communications in Algebra 44 (2016), 5223–5236 (with A. Plagne)
    DOI · arXiv:1403.0934
  33. Cauchy-Davenport type theorems for semigroups
    Mathematika 62 (2016), 1–12
    DOI · arXiv:1307.8396
  34. The Davenport constant of a box
    Acta Arith. 171 (2015), 197–220 (with A. Plagne)
    DOI · arXiv:1405.4363
  35. Small doubling in ordered semigroups
    Semigroup Forum 90 (2015), 135–148
    DOI · arXiv:1208.3233
  36. On a system of equations with primes
    J. Théor. Nombres Bordeaux 26 (2014), 399–413 (with P. Leonetti)
    DOI · arXiv:1212.0802
  37. A Cauchy-Davenport theorem for semigroups
    Uniform Distribution Theory 9 (2014), 27–42
    Online · arXiv:1210.4203
  38. On the divisibility of $a^n \pm b^n$ by powers of $n$
    Integers 13 (2013), 993–998
    Online · arXiv:1301.0131