My current research deals with combinatorics and commutative algebra.

Primary interests:

Particular interests:

A common theme in my research is the understanding of numerical or algebraic data via some underlying combinatorial structure, and I find it useful to draw ideas from other fields such as discrete geometry, algebraic geometry and algebraic topology.

Publications on Research Interests

  1. K. F. E. Chong, "Hilbert functions of colored quotient rings and a generalization of the Clements-Lindström theorem," J. Algebraic Combinatorics, vol. 42, no. 1, pp. 1--23, 2015. (preprint)
    Given a polynomial ring S = k[x1, ..., xn] over a field k, and a monomial ideal M of S, we say the quotient ring R = S/M is Macaulay-Lex if for every graded ideal of R, there exists a lexicographic ideal of R with the same Hilbert function. Clements-Lindström rings and colored squarefree rings are the two main examples of Macaulay-Lex rings. Although they 'look' very different, they are special cases of colored quotient rings, which we introduce in this paper. We completely characterize all colored quotient rings that are Macaulay-Lex, thereby simultaneously generalizing both the Clements-Lindström theorem and the Frankl-Füredi-Kalai theorem. Most notably, we construct a new class of Macaulay-Lex rings that are 'hybrids' of both Clements-Lindström rings and colored squarefree rings.
  2. K. F. E. Chong, "An application of liaison theory to the Eisenbud-Green-Harris conjecture," J. Algebra, to appear. (preprint)
    Using liaison theory, we prove that the Eisenbud-Green-Harris conjecture holds for a certain subclass of homogeneous ideals in the linkage class of a complete intersection ideal. In the case of three variables, we prove that the conjecture holds for Gorenstein ideals.
  3. K. F. E. Chong, "Generalized Macaulay representations and the flag f-vectors of generalized colored complexes," submitted. 28 pages. (preprint)
    This paper gives numerical characterizations of both the fine f-vectors of generalized colored complexes and the flag f-vectors of completely balanced Cohen-Macaulay complexes via a unified approach. As part of their proofs, we introduce the notion of Macaulay decomposability for simplicial complexes, which extends vertex-decomposability, and we generalize the notion of Macaulay representations, which has a geometric interpretation involving Macaulay decomposability.

Other Research Papers

  1. K. F. E. Chong, and K. S. R. Poh, "On Riemann Zeta Function and Twin Prime Conjecture," Proceedings of the 15th Science Research Congress, organized by Faculty of Science, National University of Singapore and Gifted Education Branch, Ministry of Education, Singapore, March 18--19, 2003.
    This is the winning research paper (grand prize) at the Singapore National Science Talent Search in 2003, and I wrote it as a high school student. The National Science Talent Search is a research-based science competition in areas including Physics, Chemistry, Biology, Computer Science, and Mathematics, and I was the first grand winner in Singapore's history to win with a math research project. The grand prize includes $10,000 cash, and a scholarship that fully funds both my undergraduate and PhD studies. The main highlight of this paper is a new characterization of when p and p+2k are simultaneously prime numbers, where k is any fixed positive integer. Note however that it does not imply the twin prime conjecture (or the more general Polignac's conjecture).
  2. K. F. E. Chong, "The Weak Order of Coxeter Systems and the Combinatorial Properties of Descent Sets," Senior Thesis, May 2009, Cornell University, Department of Mathematics, Thesis Advisor: Edward Swartz.
    This is my senior thesis that I wrote as an undergraduate student. It deals with the combinatorial properties of descent sets in relation to the weak Bruhat order of finite Coxeter systems. The main results include a generalization of a proposition in Nyman-Swartz's paper ["Inequalities for the h-vectors and flag h-vectors of geometric lattices," Discrete Comput. Geom. 32 (2004) 533-548], and a partial answer to a problem posed in Swartz's paper ["g-elements, finite buildings and higher Cohen-Macaulay connectivity," J. Combin. Theory Ser. A 113 (2006) 1305-1320].

Publications from Prior Work Experience

  1. E. Kurniawan, K. F. E. Chong, S. Sun, K. Yen, "Application of FASTAR Code in Multimedia Broadcast Multicast Service," Proceedings of IEEE 73rd Vehicular Technology Conference (VTC) Spring 2011, pp. 1--5, May 2011.
  2. E. Kurniawan, K. F. E. Chong, S. Sun, K. Yen, "Outage analysis of Joint Channel-Network Coding and its dependence on the interleaver pattern," Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC), 2011, pp. 2000--2005, Mar 2011.
  3. E. Kurniawan, S. Sun, K. Yen, and K. F. E. Chong, "Application of Network Coding in Rateless Transmission over Wireless Relay Networks," IEEE Transactions on Communications, vol. 59, no. 2, pp. 507--517, Feb 2011.
  4. E. Kurniawan, S. Sun, K. Yen, and K. F. E. Chong, "Improving error performance of Joint Channel and Network Coding in Multiple Access Relay Channel," Proceedings of the International Symposium on Information Theory and its Applications (ISITA), 2010, pp. 145--150, Oct 2010.
  5. K. F. E. Chong, E. Kurniawan, S. Sun, and K. Yen, "Fountain codes with varying probability distributions," Proceedings of the 6th International Symposium on Turbo Codes and Iterative Information Processing (ISTC), 2010, pp. 176--180, Sep 2010. (preprint)
  6. E. Kurniawan, S. Sun, K. Yen, and K. F. E. Chong, "Network Coded Transmission of Fountain Codes over Cooperative Relay Networks," Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC), 2010, pp. 1--6, Apr 2010.