Publications
Caution: These files are
preprints, and there may be differences from the published versions. The arXiv versions
are typically the most preliminary and least-polished. In a few cases (when
noted) publication errors are corrected in the .pdf files below.
- A. Benjamin, G. Levin, K. Mahlburg, J. Quinn,
"Random approaches to Fibonacci identities," The American Mathematical
Monthly 107 (2000), 511–16. link
- J. Getz, K. Mahlburg, "Partition identities and a
theorem of Zagier," Journal of Combinatorial Theory (A) 100
(2002), 27–43. pdf
- K. Mahlburg, K. Ono, "Arithmetic of certain
hypergeometric modular forms," Acta Arithmetica 113
(2004), no. 1, 39–55. pdf
- K. Mahlburg, “The overpartition function modulo small
powers of 2,” Discrete Mathematics 286 (2004), no. 3,
263–267. pdf
- K. Mahlburg, "More congruences for the
coefficients of quotients of Eisenstein series,” Journal of
Number Theory 115 (2005), no. 1, 89–99. pdf
- K. Mahlburg, "Partition congruences and the
Andrews-Garvan-Dyson crank," Proceedings of the National Academy
of Sciences 102 (2005), no. 43, 15373–76. pdf
- K. Bringmann, F. Garvan, K. Mahlburg, "Partition statistics
and quasiharmonic Maass forms", Int. Math. Res. Not., 2009,
no. 1, 63–97. arXiv:0803.1891
pdf
- K. Bringmann, K. Mahlburg, "Inequalities between
crank and rank moments", Proc. Amer. Math. Soc. 137
(2009), no. 8, 2567–2574. pdf
- K. Bringmann, K. Mahlburg, "An extension of the
Hardy-Ramanujan circle method and applications to partitions without
sequences", American Journal of Mathematics 133 (2011),
1151–1178. pdf
- T. Kemp, K. Mahlburg, A. Rattan, C. Smyth,
"Enumeration of noncrossing pairings on bit strings", Journal
of Combinatorial Theory (A) 118 (2011), 129–151. arXiv:0906.2183 pdf
- K. Bringmann, K. Mahlburg, R. Rhoades,
"Asymptotics for crank and rank moments", Bulletin of the
London Mathematical Society 43 (2011), 661–672. arXiv:0903.1297 pdf
- K. Bringmann, K. Mahlburg, "Improved bounds on
metastability thresholds and probabilities for generalized bootstrap
percolation", Transactions of the American Mathematical Society
364 (2012), 3829–3859. arXiv:1001.1977
pdf
- K. Bringmann, K. Mahlburg, A. Mellit, "Convolution
bootstrap percolation models, Markov-type stochastic processes, and mock
theta functions", International Mathematics Research Notices 2013;
971–1013. pdf
- K. Bringmann, A. Holroyd, K. Mahlburg, M. Vlasenko,
"k-run overpartitions and mock theta functions", Quarterly
Journal of Mathematics (2013), 64 (2013), 1009–1021. doi:10.1093/qmath/has019. arXiv:1203.6344 pdf
- K. Bringmann, K. Mahlburg, R. Rhoades, "Taylor
coefficients of mock-Jacobi forms and moments of partition
statistics", Mathematical Proceedings of the Cambridge
Philosophical Society, 157 (2014), 231–251. pdf
- K. Bringmann, K. Mahlburg, "Asymptotic
formulas for coefficients of Kac-Wakimoto characters",
Mathematical Proceedings of the Cambridge Philosophical Society 155
(2013), 51–72. pdf
- K. Bringmann, K. Mahlburg, "Asymptotic
inequalities for positive crank and rank moments", Transactions of
the American Mathematical Society 366 (2014), 1073–1094. arXiv:1205.2155 pdf
Note: The published version of this paper has an incorrect proof
of Corollary 3.4. The linked .pdf file corrects the error (p. 11-12).
- K. Bringmann, A. Folsom, K. Mahlburg,
"Quasimodular forms and $s\ell(m|m)^\wedge$ characters", Ramanujan
Journal 36 (2015), 103–116. arXiv:1302.4040 pdf
Update: “Correction to:
Quasimodular forms and $s\ell(m|m)∧\wedge$ characters”, Ramanujan Journal 47 (2018), no. 1, 237–241. pdf
- K. Mahlburg, C. Smyth, "Symmetric polynomials and
symmetric mean inequalities", Electronic Journal of Combinatorics 20
(2013), P34, 14 pp. pdf
- K. Bringmann, J. Lovejoy, K. Mahlburg, "On
q-difference equations for partitions without k-sequences",
Proceedings of The Legacy of Ramanujan Conference, Ramanujan Mathematical
Society Lecture Notes 20, 2013, pp. 129–137. pdf
- M. Di Nasso, I. Goldbring, R. Jin, S. Leth, M. Lupini,
K. Mahlburg, "On a sumset conjecture of Erdös",
Canadian Journal of Mathematics 67 (2015), 795–809.
dx.doi.org/10.4153/CJM-2014-016-0. arXiv:1307.0767 pdf
- K. Bringmann, K. Mahlburg, "Asymptotic formulas
for stacks and unimodal sequences", Journal of Combinatorial
Theory (A) 126 (2014), 194–215. arXiv:1308.6813 pdf
- M. Di Nasso, I. Goldbring, R. Jin, S. Leth, M. Lupini,
K. Mahlburg, "High density piecewise syndeticity of sumsets", Advances
in Mathematics 278 (2015), 1–33. arXiv:1310.5729 pdf
- G. Andrews, K. Bringmann, K. Mahlburg, "Double
series representation for Schur's partition function and related
identities", Journal of Combinatorial Theory (A) 132
(2015), 102–119. arXiv:1405.3345 pdf
- K. Bringmann, K. Mahlburg, "False theta functions
and companions to Capparelli's identities", Advances in
Mathematics 278 (2015), 121–136. arXiv:1404.3113 pdf
- K. Bringmann, K. Mahlburg, K. Nataraj, "Distinct
parts partitions without sequences", Electronic Journal of
Combinatorics 22 (2015), Paper 3.3, 13 pp. arXiv:1501.02305 pdf
- K. Bringmann, J. Dousse, J. Lovejoy, K. Mahlburg,
"Overpartitions with restricted odd differences", Electronic
Journal of Combinatorics 22 (2015), Paper 3.17, 16 pp. pdf
Note: The published version has
typos on p. 7, where several (k+1)’s should be k’s. This is corrected on
p.8 of the linked file.
- K. Bringmann, J. Lovejoy, K. Mahlburg, "A
partition identity and the universal mock theta functions $g_2$", Mathematical
Research Letters 23 (2016), 67–80. arXiv:1311.5483 pdf
- M. Di Nasso, I. Goldbring, R. Jin, S. Leth, M. Lupini,
K. Mahlburg, "A monad measure space for logarithmic density", Monatshefte
für Mathematik 181 (2016), 577–599. arXiv:1503.03810 pdf
- M. Di Nasso, I. Goldbring, R. Jin, S. Leth, M. Lupini,
K. Mahlburg, "High density piecewise syndeticity of product sets in
amenable groups," Journal of Symbolic Logic 81 (2016),
1555–1562. arXiv:1505.04701 pdf
- M. Di Nasso, I. Goldbring, R. Jin, S. Leth, M. Lupini,
K. Mahlburg, "Approximate polynomial structure in additively large
sets," INTEGERS - Electronic Journal of Combinatorial Number
Theory 16 (2016), Paper No. A49, 11 pp. arXiv:1508.02350 pdf
- K. Bringmann, K. Mahlburg, A. Milas, "The
Lusztig-Macdonald-Wall conjectures and q-difference equations", Lie
Algebras, Vertex Operator Algebras, and Related Topics, p.41–49,
Contemporary Mathematics 695, American Mathematical Society,
Providence, R.I. 2017. pdf
- K. Bringmann and K. Mahlburg, "Three-colored
partitions and dilated companions of Capparelli's identities",
Analytic number theory, modular forms, and q-hypergeometric series,
139-56, Springer Proc. in Math. and Stat. 221, 2017. pdf
- K. Bringmann, C. Jennings-Shaffer, K. Mahlburg,
"On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a
variation of Ramanujan's $\omega(q)$," Advances in Mathematics
325 (2018), 505–532. arXiv:1612.08219 pdf
- K. Bringmann, C. Jennings-Shaffer, K. Mahlburg, R.
Rhoades, "Peak positions of strongly unimodal sequences”, Transactions of the American
Mathematical Society 273 (2019),
7087-7019. arXiv:1806.03217 pdf
- K. Bringmann, K. Mahlburg, A. Milas, "On
characters of $L_{\frak{sl}_n}(-\Lambda_0)$-modules$,” Communications in Contemporary
Mathematics 22
(2020), 1950030, 22 pp. arXiv:1803.08029 pdf
- K. Bringmann, C. Jennings-Shaffer, K.
Mahlburg, "Proofs and reductions of various conjectured partition
identities of Kanade and Russell”, Journal
für die reine und angewandte Mathematik (Crelle’s Journal) 766 (2020), 109-135. arXiv:1809.06089 pdf
- K. Bringmann, K. Mahlburg, A. Milas,
“Quantum modular forms and plumbing graphs of 3-manifolds”, Journal of Combinatorial Theory (A) 170 (2020), 105145, 32 pp. arXiv:1810.05612 pdf
- K. Bringmann, K. Mahlburg, A. Milas, “Higher
depth quantum modular forms and plumbed 3-manifolds”, Letters in
Mathematical Physics 110 (2020), 2675-2702. arXiv:1906.10722
- K. Bringmann, C. Jennings-Shaffer, K.
Mahlburg, “On a Tauberian theorem of Ingham and Euler-Maclaurin
Summation”, to appear in The Ramanujan Journal. arXiv:1910.03036
- K. Bringmann, C. Jennings-Shaffer, K. Mahlburg,
“The Asymptotic Distribution of the Rank for Unimodal Sequences”, Journal
of Number Theory 229 (2021), 444-462. arXiv:1910.10790
Other writing, including surveys, unpublished works, and Ph.D. Thesis:
- K.
Mahlburg, “Ranks
and Cranks”, to appear in the Encyclopedia of Ramanujan and His
Mathematics, Springer.
- K. Mahlburg, “Honoring a
Gift from Kumbakonam”, to appear in the Encyclopedia of Ramanujan and His
Mathematics, Springer.
- K.
Bringmann, K. Mahlburg, "Schur's second partition theorem and mixed
mock modular forms". arXiv:1307.1800
- K. Mahlburg, "An overview of braid group
cryptography", 2004. (unpublished graduate school project) pdf
- K. Mahlburg, "Congruences for the coefficients of
modular forms and applications to number theory," Ph.D. Thesis,
University of Wisconsin-Madison, 2006. pdf
Note: This largely consists of the
results found in papers 4, 5, and
6 above.
Return to Karl
Mahlburg’s homepage.