{"id":125,"date":"2019-06-24T11:42:33","date_gmt":"2019-06-24T15:42:33","guid":{"rendered":"http:\/\/khaymake.clasit.org\/?page_id=125"},"modified":"2025-04-07T10:19:16","modified_gmt":"2025-04-07T14:19:16","slug":"research","status":"publish","type":"page","link":"https:\/\/khaymake.clasit.org\/?page_id=125","title":{"rendered":"Research"},"content":{"rendered":"\n<p>My research is on applications of discrete mathematics and coding theory.<\/p>\n\n\n\n<p><strong>Publications<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>K. Haymaker, E. McMillon. Parity-check Codes from Disjunct Matrices. Advances in Mathematics of Communications, 2025. <a href=\"https:\/\/www.aimsciences.org\/\/article\/doi\/10.3934\/amc.2024034\">https:\/\/www.aimsciences.org\/\/article\/doi\/10.3934\/amc.2024034<\/a><\/li>\n\n\n\n<li>Diaz-Lopez, A., Haymaker, K., McGarry, C., McMahon, D. Metrics on permutations with the same descent set. <em>The PUMP Journal of Undergraduate Research, 8<\/em>, 57-69, 2025. <a href=\"https:\/\/journals.calstate.edu\/pump\/article\/view\/4157\">https:\/\/journals.calstate.edu\/pump\/article\/view\/4157<\/a><\/li>\n\n\n\n<li>Haymaker, K., Tait, M., Timmons, C. Hypergraphs of girth 5 and 6 and coding theory. (submitted) <a href=\"https:\/\/arxiv.org\/abs\/2404.01839\">https:\/\/arxiv.org\/abs\/2404.01839<\/a><\/li>\n\n\n\n<li>A. Diaz-Lopez, K. Haymaker, K. Keough, J. Park, E. White. Metrics on Permutations with the Same Peak Set. <em>Involve, a Journal of Mathematics<\/em>, 2024. <a href=\"https:\/\/msp.org\/involve\/2024\/17-5\/involve-v17-n5-p06-p.pdf\">https:\/\/msp.org\/involve\/2024\/17-5\/involve-v17-n5-p06-p.pdf<\/a><\/li>\n\n\n\n<li>K. Haymaker, J. O\u2019Pella. Coding Theory and Pooled Testing for COVID-19. <em>Mathematics Magazine<\/em> (accepted to appear)<\/li>\n\n\n\n<li>A. Diaz-Lopez, K. Haymaker, M. Tait. Spectral radii of arithmetical structures on cycle graphs. <em>Linear and Multilinear Algebra<\/em> (accepted to appear)<\/li>\n\n\n\n<li>K. Haymaker, H. Lopez, B. Malmskog, G.L. Matthews, F. Pinero, Mathematical LoRE: Local Recovery of Erasures. <em>IEEE BITS: The Information Theory Magazine<\/em>, 2024. <a href=\"https:\/\/ieeexplore.ieee.org\/document\/10416362\">https:\/\/ieeexplore.ieee.org\/document\/10416362<\/a><\/li>\n\n\n\n<li>K. Haymaker, B. Malmskog, and G. L. Matthews, Algebraic hierarchical locally recoverable codes with nested affine subspace recovery, Designs, Codes and Cryptography, 2024. <a href=\"https:\/\/link.springer.com\/article\/10.1007\/s10623-024-01510-x\">https:\/\/link.springer.com\/article\/10.1007\/s10623-024-01510-x<\/a><\/li>\n\n\n\n<li>K. F. Benson,&nbsp;J. Bolkema,&nbsp;K. Haymaker,&nbsp;C. Kelley,&nbsp;S. R. Kingan,&nbsp;G. L. Matthews&nbsp;&amp;&nbsp;E. L. N\u0103stase. Analysis of Termatiko Sets in Measurement Matrices. <em>Research Trends in Graph Theory and Applications <\/em>(vol. 25, pp. 51-71), 2021.&nbsp;<\/li>\n\n\n\n<li>A. Petrosino, A. Schembor, and K. Haymaker. Counting profile strings from rectangular tilings, <em>Involve, a Journal of Mathematics<\/em>, 2020. <\/li>\n\n\n\n<li>K. Haymaker and J. O&#8217;Pella. LRCs from Planar Graphs,<em> Journal of Algebra, Combinatorics, Discrete Structures, and Applications <\/em><a href=\"https:\/\/jacodesmath.com\/index.php\/jacodesmath\/article\/view\/111\">https:\/\/jacodesmath.com\/index.php\/jacodesmath\/article\/view\/111<\/a>, 2020. <\/li>\n\n\n\n<li>A. Beemer, K. Haymaker, C.A. Kelley. Absorbing sets of codes from \ffinite geometries. Cryptography and Communications, 2019.<\/li>\n\n\n\n<li> B. Malmskog, K. Haymaker. What (Quilting) Circles can be Squared? Mathematics Magazine, June 2019.<\/li>\n\n\n\n<li> K. Haymaker, B. Malmskog, G. Matthews, Locally Recoverable Codes with Availability t&gt;=2 from Fiber Products of Curves. Advances in Mathematics of Communications, 2018.<\/li>\n\n\n\n<li>C. Meyer, K. Haymaker, and C.A. Kelley. Coding for multilevel and partial erasure channels. Advances in Mathematics of Communications, 2018.<\/li>\n\n\n\n<li>K. Haymaker. Absorbing set analysis of codes from affine planes. Lecture Notes in Computer Science book series, Springer, 2017.<\/li>\n\n\n\n<li>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.<\/li>\n\n\n\n<li>K. Haymaker, S. Robertson. Counting Colorful Tilings of Rectangular Arrays. Journal of Integer Sequences, 2017.<\/li>\n\n\n\n<li>N. A. Corwin and K. Haymaker. Graph groups that are subgroups of Thompson&#8217;s group V . International Journal of Algebra and Computation, 2016.<\/li>\n\n\n\n<li>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.<\/li>\n\n\n\n<li>K. Haymaker and C.A. Kelley. Covering codes for multilevel flash memories. Proceedings of the Asilomar Conference on Signals, Systems, and Computing, 2012.<\/li>\n\n\n\n<li>K. Haymaker and C.A. Kelley. Geometric WOM codes and coding strategies for multilevel Flash memories. Designs, Codes and Cryptography, 2012.<\/li>\n\n\n\n<li>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.<\/li>\n<\/ul>\n\n\n\n<p>My PhD research was completed under the supervision of <a href=\"https:\/\/www.math.unl.edu\/~ckelley2\/\" target=\"_blank\" rel=\"noreferrer noopener\">Dr. Christine Kelley<\/a> at the University of Nebraska-Lincoln in 2014.<\/p>\n\n\n\n<p>I received Villanova University Summer Grants to support my research in 2024 and 2016.<\/p>\n\n\n\n<p>I worked on the following projects with Villanova students:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(Joint with Dr. Alexander Diaz-Lopez) Permutation metrics and descent sets, Fall 2022-Summer 2023<\/li>\n\n\n\n<li>Group testing schemes from codes, Fall 2022<\/li>\n\n\n\n<li>(Joint with Dr. Alexander Diaz-Lopez) Permutation metrics and peak sets, Spring &amp; Summer 2021 <\/li>\n\n\n\n<li>Counting profiles from rectangular tilings, Spring 2020<\/li>\n\n\n\n<li>Locally recoverable codes from planar graphs, 2018-2019<\/li>\n\n\n\n<li>Enumerating tilings, summer 2016<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>My research is on applications of discrete mathematics and coding theory. Publications: 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:<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/full-width.php","meta":{"footnotes":""},"class_list":["post-125","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/pages\/125","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=125"}],"version-history":[{"count":22,"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/pages\/125\/revisions"}],"predecessor-version":[{"id":280,"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/pages\/125\/revisions\/280"}],"up":[{"embeddable":true,"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=\/wp\/v2\/pages\/2"}],"wp:attachment":[{"href":"https:\/\/khaymake.clasit.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=125"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}