My Co-Authors (12)

Charlotte Aten, Alexander Clifton, Bishal Deb, Yifeng Huang, Jeong Han Kim, Sangjib Kim, Seoyoung Kim(2), Young-Hun Kim, Ben Lund, Thang Pham(2), Sam Spiro, Chi Hoi Yip(2)

Preprints

1.  Diophantine tuples and multiplicative structure of shifted multiplicative subgroups (with Seoyoung Kim, and Chi Hoi Yip) 

We provide an improvement on a result by Dixit, Kim, and Murty (2022) on the largest size of a generalized Diophantine tuple with property D_k(n). We also make progress towards a conjecture of Sárközy on multiplicative decompositions of shifted multiplicative subgroups.

2.  Intersection patterns and incidence theorems (with Thang Pham) 

We study the finite field analog of some questions studied by Mattila from geometric measure theory with an emphasis on the group of orthogonal matrices and the set of orthogonal projections. This presents applications of the Erdős-Falconer distance problem over finite fields.

3.  Weak Bruhat interval modules of the 0-Hecke algebras for genomic Schur functions (with Young-Hun Kim)  

We provide a representation theoretic interpretation of certain symmetric functions, which originated from K-theory. More precisely, we construct 0-Hecke modules corresponding to genomic Schur functions introduced by Pechenik and Yong (2017).

4.  Orientable triangulable manifolds are essentially quasigroups (with Charlotte Aten)  

We construct a functor from n-ary analogues of quasigroups to orientable triangulable n-dimensional manifolds, which generalizes the functor described by Herman and Pakianathan (2017) from nonabelian finite groups to tessellated surfaces. 

Accepted & Published Papers

1.  Explicit constructions of Diophantine tuples over finite fields (with Seoyoung Kim and Chi Hoi Yip), to appear in The Ramanujan Journal. 

By explicit constructions, we improve the lower bound on the largest size of a Diophantine tuple over a finite field.

2.  Combinatorics of Euclidean spaces over finite fields*, (The alignment of the paper in arxiv is better), Annals of Combinatorics, vol 28, 283–327, (2024).  

We develop the Euclidean analogs of q-binomial coefficients, and study their combinatorics. This is the theory of the orthogonal group version of q-analogs.

3.  Continuously increasing subsequences of random multiset permutations (with Alexander Clifton, Bishal Deb, Yifeng Huang, and Sam Spiro), European Journal of Combinatorics, vol. 110 (2023), 103708  

We give an exact formula for the expected values of the longest continuously increasing subsequences in random words, and use this to obtain asymptotics, confirming a conjecture of Diaconis, Graham, He, and Spiro (2021). The proof for the exact formula involves a non-trivial argument from generating functions. 

4.  Threshold functions for incidence properties in finite vector spaces (with Jeong Han Kim, Ben Lund, and Thang Pham), Finite Fields and Their Applications, vol. 87 (2023), 102149  

We provide threshold functions for the event that a random subset of the points of a vector space over a finite field has certain properties related to point-flat incidences.

5.  Graphs associated with orthogonal collections of k-planes over finite fields*, Discrete Mathematics, vol. 344 (2021), no. 9, 112496 

We construct graphs coming from quadratic spaces over finite fields which generalize a result given by Bishnoi, Ihringer, and Pepe (2020). The graphs have an unexpected relation with lower bounds of off-diagonal Ramsey numbers.

6.  Incidences between Euclidean subspaces over finite fields*, Forum Mathematicum, vol. 33 (2021), no. 4, 1051-1059 

We study the incidences between Euclidean spaces over finite fields using the Expander mixing lemma.

7.  Pieri and Littlewood-Richardson rules for two rows and cluster algebra structure** (with Sangjib Kim), Journal of Algebraic Combinatorics, vol. 45, no. 3, 887-909, (2017) 

We prove that the twice-iterated Pieri algebra has the structure of a cluster algebra of type A and investigate its relation with the tensor product decomposition problem.

Conference Proceedings

1.  Weak Bruhat interval modules of the 0-Hecke algebras for genomic Schur functions (with Young-Hun Kim), Séminaire Lotharingien de Combinatoire, 89B.54 (2023)

2.  Continuously increasing subsequences of random multiset permutations (with Alexander Clifton, Bishal Deb, Yifeng Huang, and Sam Spiro), Séminaire Lotharingien de Combinatoire, 86B.4 (2022)

Thesis

   Combinatorics of quadratic spaces over finite fields, Ph.D. thesis (2021)

    The three * papers above constitute my Ph.D. thesis.

   Cluster algebra structure of certain quadratic algebras, Master's thesis (2016)

     My Master's thesis contains a result in the paper ** above.