Dr. Jia Huang | University of Nebraska at Kearney

Areas of Expertise

Discrete Mathematics
Math

Employment

Professor, Department of Mathematics and Statistics, University of Nebraska at Kearney, 2023--present

Associate Professor, Department of Mathematics and Statistics, University of Nebraska at Kearney, 2018--2023

Assistant Professor, Department of Mathematics and Statistics, University of Nebraska at Kearney, 2014--2018

Postdoctoral Associate, School of Mathematics, University of Minnesota-Twin Cities, 2013--2014

Education

Ph.D. in Mathematics, University of Minnesota-Twin Cities

B.S. in Mathematics and Applied Mathematics, University of Science and Technology of China

Teaching

Current Teaching (Fall 2024)

MATH 102 Colledge Algebra, MATH 413 Discrete Mathematics, MATH 460 Advanced Calculus I
Course materials and other useful resources are available on Canvas.
Office hours: MWF 10:00AM--11:10AM, 2:30PM--3:15PM or by appointment

Courses Taught at UNK

MATH 102 College Algebra, MATH 103 Plane Trigonometry, MATH 120 Finite Mathematics, MATH 123 Applied Calculus I, MATH 115 Calculus I with Analytic Geometry, MATH 202 Calculus II with Analytic Geometry, MATH 250 Foundations of Math, MATH 260 Calculus III, MATH 280 Linear Algebra, MATH 310 College Geometry, MATH 350 Abstract Algebra, MATH 365 Complex Analysis, MATH 400 History of Mathematics, MATH 404 Theory of Numbers, MATH 413 Discrete Mathematics, MATH 460 Advanced Calculus I, MATH 864 Geometry for Teachers (new course development)

Courses Taught at the University of Minnesota

MATH 1272 Calculus II, MATH 1372 CSE Calculus II, MATH 2263 Multivariable Calculus

Research

My research interests include Discrete Mathematics and its connections with other fields (more specifically, Algebraic and Enumerative Combinatorics, Combinatorial Representation Theory, and Graph Theory).

I received my Ph.D. at the University of Minnesota under the supervision of Professor Victor Reiner. My Thesis is 0-Hecke algebra actions on flags, polynomials, and Stanley-Reisner rings.

I use mathematics software such as GAP, Magma, and Sage in my research.

I am the organizer for the annual UNK Undergraduate Research Mathematics Mini-Symposium: 2017, 2018, 2019, 2020 (canceled due to COVID), 2022, 2023, 2024.

Recent Presentations:

Associative-commutative spectra for some varieties of groupoids (joint work with E. Lehtonen), International Conference on Enumerative Combinatorics and Applications (Virtual), August 2024.
Partially palindromic compositions, AMS Fall Central Sectional Meeting, Omaha, October 2023.
Partially Palindromic Compositions, International Conference on Enumerative Combinatorics and Applications (ICECA), September 2023.
The associative-Commutative spectrum of a binary operation (joint work with E. Lehtonen), The 35th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC), UC Davis, July 2023.
Norton algebras of some distance regular graphs, Graph Theory, Algebraic Combinatorics and Mathematical Physics, Centre de recherches mathématiques (CRM), Université de Montréal, August 2022.
The Norton algebras of some distance regular graphs, Discrete Mathematics Seminar, Texas State University, November 2020.
Integer Tillings and Domination Ratio, Combinatorics and Graph Theory Seminar, Anhui University, June 2019.
Variations of the Catalan number from nonassociative binary operations, Combinatorics Seminar, University of Wisconsin, April 2019.
Ordered set partitions and the 0-Hecke algebra, The 30th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC), Dartmouth College, July 2018.
An improved upper bound for the bondage number of graphs on surfaces, Graph Theory and Combinatorial Network Theory Conference, Beijing Normal University, June 2018.
Polynomial invariants of finite groups of sparse matrices, Public Talk, Beijing Normal University, June 2018.
Critical groups for Hopf algebra modules, Great Plains Combinatorics Conference, Kansas State University, April 2018.

Recent Publications:

J. Huang, Dissociation in circulant graphs and integer distance graphs, Discussiones Mathematicae Graph Theory 45(3) (2025) 927--942.
J. Huang and E. Lehtonen, Associative-commutative spectra for some varieties of groupoids, Enumerative Combinatorics and Applications 4:4 (2024), Article S2R29.
J. Huang, Even and odd compositions with restricted parts, Journal of Integer Sequences 27 (2024), Article 24.6.5.
J. Huang and E Lehtonen, The associative-commutative spectrum of a binary operation, Discrete Mathematics 346 (2023), Paper No. 113535, 22 pp.
J. Huang, Partially Palindromic Compositions, Journal of Integer Sequences 26 (2023), Article 23.4.1.
J. Huang, Domination ratio of a family of integer distance digraphs with arbitrary degree, Discrete Applied Mathematics 317 (2022), 1–9
N. Hein and J. Huang, Variations of the Catalan numbers from some nonassociative binary operations, Discrete Mathematics 345 (2022), Paper No. 112711, 18 pp.
J. Huang, Norton algebras of the Hamming Graphs via linear characters, Electronic Journal of Combinatorics 28 (2021), #P2.30, 36 pp.
J. Huang, Nonassociativity of the Norton algebras of some distance regular graphs, Electronic Journal of Combinatorics 27 (2020), #P4.27, 22pp.
J. Huang, Hecke algebras of simply-laced type with independent parameters, Algebraic Combinatorics 3 (2020), no.~3, 667--691.
J. Huang, Compositions with restricted parts, Discrete Mathematics 343 (2020), Paper No. 111875, 9 pp.
D. Grinberg, J. Huang, and V Reiner, Critical groups for Hopf algebra modules, Mathematical Proceedings of the Cambridge Philosophical Society 168 (2020), 473--503.
J. Huang, Domination ratio of integer distance digraphs, Discrete Applied Mathematics 262 (2019), 104–115.
J. Huang, B. Rhoades, and T. Scrimshaw, Hall-Littlewood polynomials and a Hecke action on ordered set partitions, Proceedings of the American Mathematical Society 147 (2019), 1839--1850.
J. Huang and J. Shen, New upper bounds for the bondage number of a graph in terms of its maximum degree and Euler characteristic, Ars Combinatoria 140 (2018) 373--387.
J. Huang and B. Rhoades, Ordered set partitions and the 0-Hecke algebra, Algebraic Combinatorics 1 (2018), 47--80.
J. Huang, M. Mickey, and J. Xu, The nonassociativity of the double minus operation, Journal of Integer Sequences 20 (2017), Article 17.10.3.
J. Huang, A uniform generalization of some combinatorial Hopf algebras, Algebras and Representation Theory 20 (2017) 379--431.
J. Huang, J. Lewis, and V Reiner, Absolute order in general linear groups, Journal of the London Mathematical Society 95 (2017) 223--247.

See also my Google Scholar profile and my ResearchGate profile.

Student Research:

I have mentored the following students through UNK's Undergraduate Research Fellows program:

Gamaliel Montero Alcaraz, 2019--2020
Evan Olson, 2018--2019 (currently a graduate student at University of Kansas)
Jianbai Xu, 2016--2017 (his presentation, his master thesis later at University of Windsor, and his LinkedIn profile)
Madison Mickey, 2016--2017 (her presentation in the Undergraduate Research Mathematics Mini-Symposium)
Chenli Huang, Fall 2016