Research

My research is on applications of discrete mathematics and coding theory.

Publications:

  • K. Haymaker, E. McMillon. Parity-check Codes from Disjunct Matrices. Advances in Mathematics of Communications, 2025. https://www.aimsciences.org//article/doi/10.3934/amc.2024034
  • Diaz-Lopez, A., Haymaker, K., McGarry, C., McMahon, D. Metrics on permutations with the same descent set. The PUMP Journal of Undergraduate Research, 8, 57-69, 2025. https://journals.calstate.edu/pump/article/view/4157
  • Haymaker, K., Tait, M., Timmons, C. Hypergraphs of girth 5 and 6 and coding theory. (submitted) https://arxiv.org/abs/2404.01839
  • A. Diaz-Lopez, K. Haymaker, K. Keough, J. Park, E. White. Metrics on Permutations with the Same Peak Set. Involve, a Journal of Mathematics, 2024. https://msp.org/involve/2024/17-5/involve-v17-n5-p06-p.pdf
  • K. Haymaker, J. O’Pella. Coding Theory and Pooled Testing for COVID-19. Mathematics Magazine (accepted to appear)
  • A. Diaz-Lopez, K. Haymaker, M. Tait. Spectral radii of arithmetical structures on cycle graphs. Linear and Multilinear Algebra (accepted to appear)
  • K. Haymaker, H. Lopez, B. Malmskog, G.L. Matthews, F. Pinero, Mathematical LoRE: Local Recovery of Erasures. IEEE BITS: The Information Theory Magazine, 2024. https://ieeexplore.ieee.org/document/10416362
  • K. Haymaker, B. Malmskog, and G. L. Matthews, Algebraic hierarchical locally recoverable codes with nested affine subspace recovery, Designs, Codes and Cryptography, 2024. https://link.springer.com/article/10.1007/s10623-024-01510-x
  • K. F. Benson, J. Bolkema, K. Haymaker, C. Kelley, S. R. Kingan, G. L. Matthews & E. L. Năstase. Analysis of Termatiko Sets in Measurement Matrices. Research Trends in Graph Theory and Applications (vol. 25, pp. 51-71), 2021. 
  • A. Petrosino, A. Schembor, and K. Haymaker. Counting profile strings from rectangular tilings, Involve, a Journal of Mathematics, 2020.
  • K. Haymaker and J. O’Pella. LRCs from Planar Graphs, Journal of Algebra, Combinatorics, Discrete Structures, and Applications https://jacodesmath.com/index.php/jacodesmath/article/view/111, 2020.
  • A. Beemer, K. Haymaker, C.A. Kelley. Absorbing sets of codes from finite geometries. Cryptography and Communications, 2019.
  • B. Malmskog, K. Haymaker. What (Quilting) Circles can be Squared? Mathematics Magazine, June 2019.
  • K. Haymaker, B. Malmskog, G. Matthews, Locally Recoverable Codes with Availability t>=2 from Fiber Products of Curves. Advances in Mathematics of Communications, 2018.
  • C. Meyer, K. Haymaker, and C.A. Kelley. Coding for multilevel and partial erasure channels. Advances in Mathematics of Communications, 2018.
  • K. Haymaker. Absorbing set analysis of codes from affine planes. Lecture Notes in Computer Science book series, Springer, 2017.
  • A. Barg, K. Haymaker, E. Howe, G. Matthews, A. Varilly-Alvarado. Locally recoverable codes from algebraic curves and surfaces. Proceedings of the 2016 IPAM Workshop on Algebraic Geometry for Cryptography and Coding Theory, 2017.
  • K. Haymaker, S. Robertson. Counting Colorful Tilings of Rectangular Arrays. Journal of Integer Sequences, 2017.
  • N. A. Corwin and K. Haymaker. Graph groups that are subgroups of Thompson’s group V . International Journal of Algebra and Computation, 2016.
  • K. Haymaker and C.A. Kelley. Structured bit-interleaved LDPC codes for MLC flash memory. IEEE Journal on Selected Areas of Communications (JSAC), Special Issue on Communication Methodologies for the Next-Generation Storage Systems, 2014.
  • K. Haymaker and C.A. Kelley. Covering codes for multilevel flash memories. Proceedings of the Asilomar Conference on Signals, Systems, and Computing, 2012.
  • K. Haymaker and C.A. Kelley. Geometric WOM codes and coding strategies for multilevel Flash memories. Designs, Codes and Cryptography, 2012.
  • K. Haymaker and C.A. Kelley. Coding strategies for reliable storage in multilevel flash memories. In Proceedings of the International Castle Meeting on Coding Theory and Applications (3ICMCTA), Cardona, Spain, 2011.

My PhD research was completed under the supervision of Dr. Christine Kelley at the University of Nebraska-Lincoln in 2014.

I received Villanova University Summer Grants to support my research in 2024 and 2016.

I worked on the following projects with Villanova students:

  • (Joint with Dr. Alexander Diaz-Lopez) Permutation metrics and descent sets, Fall 2022-Summer 2023
  • Group testing schemes from codes, Fall 2022
  • (Joint with Dr. Alexander Diaz-Lopez) Permutation metrics and peak sets, Spring & Summer 2021
  • Counting profiles from rectangular tilings, Spring 2020
  • Locally recoverable codes from planar graphs, 2018-2019
  • Enumerating tilings, summer 2016