L-R: Bruce Berndt, George Andrews (my PhD advisor), Ken Ono, and yours truly. Photo from June 7, 2024 at the Legacy of Ramanujan 2024: Celebrating the 85th birthdays of George Andrews and Bruce Berndt

Research

My research interests are integer partitions, q-series, generating functions, and some polyhedral geometry.

Below: The three-dimensional integer lattice point representation of the set of partitions of 26 into parts of sizes 1, 2, and 5. The components of the vectors indicate the multiplicity of each part size. (26,0,0) is 26 parts of size 1; (1,0,5) is one part of size 1 and five parts of size 5; and (0,13,0) is 13 parts of size 2.

Publications

G. Gray, D. Hovey, B. Kronholm, E. Payne, H. Swisher, R. Watson. A generalization of Franklin’s partition identity and a Beck-type companion identity. The Ramanujan Journal, 67(100), July, 2025. https://doi.org/10.1007/s11139-025-01121-7.
D. Eichhorn and B. Kronholm. Supercranks for partitions with a fixed number of parts. Journal of Algebraic Combinatorics, 62(3), April, 2025. https://doi.org/10.1007/s10801-025-01413-7. https://rdcu.be/ewnUm
J. Aniceto and B. Kronholm. Hansraj Gupta’s “A Technique in Partitions” revisited: congruences, cranks, and polyhedral geometry. International Journal of Number Theory, 21(03):639–655, January 2025. https://doi.org/10.1142/S1793042125500320.
D. Eichhorn, A. Larsen, and B. Kronholm. Cranks for partitions with bounded largest part. Proc. Amer. Math. Soc., 151(8):3291–3303, August 2023.
J. Gregory, B. Kronholm, and J. White. Iterated Rascal triangles. Aequationes Mathematicae, https://doi.org/10.1007/s00010-023-00987-6, August 2023.
D. Eichhorn, L. Engle, and B. Kronholm. Congruences for consecutive coefficients of Gaussian polynomials with crank statistics. Electronic J. Combinatorics, 29(4):P4.38, 2022.
A. Castillo, S. Flores, A. Hernandez, B. Kronholm, A. Larsen, and A. Martinez. Quasipolynomials and maximal coefficients of Gaussian polynomials. Ann. Comb., 23(3-4):589–611, November 2019.
B. Kronholm and J. Schmidt. A bijection between the set of odd numbers under the accelerated Collatz function and the set of odd numbers. The Pi Mu Epsilon Journal, 2019.
B. Kronholm and J. Rehmert. A generalization of congruence properties for a restricted partition function. INTEGERS, (#A22), March 2018.
B. Kronholm. On congruence properties of the coefficients of Gaussian polynomials. Proc. Amer. Math. Soc., 147:489–495, 2018.
F. Breuer, D. Eichhorn, and B. Kronholm. Polyhedral geometry, supercranks, and combinatorial witnesses of congruence properties of partitions into three parts. European Journal of Combinatorics, 65:230–252, June 2017.
F. Breuer and B. Kronholm. A polyhedral model of partitions with bounded differences and a bijective proof of a theorem of Andrews, Beck, and Robbins. Research in Number Theory, 2(2):1–15, March 2016.
B. Kronholm and A. Larsen. Symmetry and divisibility properties of the generating function for the restricted partitions of n into exactly m parts modulo any prime. Annals of Combinatorics, 19(4):735–747, December 2015.
B. Kronholm. Generalized congruence properties of the restricted partition function p(n, m). The Ramanujan Journal, 30(3):425–436, April 2013.
B. Kronholm. A result on Ramanujan-like congruence properties of the restricted partition function p(n,m) across both variables. INTEGERS, (#A63):1–6, November 2012.
B. Kronholm. On congruence properties of consecutive values of p(n,m). INTEGERS, (#A16):1–6, March 2007.
B. Kronholm. On congruence properties of p(n, m). Proc. Amer. Math. Soc., 133(10):2891–2895, April 2005.

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