** 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.

- 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), - 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

- 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

- 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.*.*arXiv:1203.6344

- 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.

- 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

*Note*:*The published version of this paper has an incorrect proof of Lemma 3.4. The linked .pdf file corrects the error.*

- 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.

- 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$,” to appear in
*Communications in Contemporary Mathematics.*arXiv:1803.08029 pdf

- K. Bringmann, C.
Jennings-Shaffer, K. Mahlburg, "Proofs and
reductions of various conjectured partition identities of Kanade and Russell”, to appear in
*Journal für die reine und angewandte Mathematik (Crelle’s Journal).*arXiv:1809.06089 pdf

- K. Bringmann, K. Mahlburg, A. Milas, “Quantum
modular forms and plumbing graphs of 3-manifolds”, to appear in
*Journal of Combinatorial Theory (A)***170**(2020). arXiv:1810.05612 pdf

Preprints

- K. Bringmann, K.
Mahlburg, A. Milas, “Higher depth quantum modular forms and plumbed
3-manifolds”, submitted for publication. arXiv:1906.10722
- K. Bringmann,
C. Jennings-Shaffer, K. Mahlburg, “On a Tauberian theorem of Ingham and Euler-Maclaurin
Summation”, preprint. arXiv:1910.03036
- K. Bringmann,
C. Jennings-Shaffer, K. Mahlburg, “The
Asymptotic Distribution of the Rank for Unimodal Sequences”, preprint. 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.