Publications and Curriculum Vitae
Publications and Curriculum Vitae
See my c.v. for abstracts. For some of the older papers, I have official reprints from the journal; email me (tchow AT alum DOT mit DOT edu) if you want them. If the format of the files below gives you trouble, try the arXiv for math and cs preprints, where I’ve submitted some of these papers and where several file formats are available. Note that the versions below may contain minor improvements of the arXiv versions.
If you have access to MathSciNet, you can click
here to read Mathematical Reviews I’ve written.
T. Chow The Latin tableau conjecture, preprint.
T. Chow A well-motivated proof that pi is irrational, preprint.
T. Chow Cooking poisons: thinking laterally with game theory, Mathematics Magazine, to appear.
L. Barnes, S. Cameron, T. Chow, E. Cohen, K. Frankston, B. Howard, F. Kochman, D. Scheinerman, and J. VanderKam, Efficient unbiased sparsification, ISIT 2024, WE2.R2.4. DOI 10.1109/ISIT57864.2024.10619383
T. Chow, A mathematician reads the kalam cosmological argument, Math. Intell. 45 (2023), 150–158.
T. Chow, Digraph analogues of the Tutte polynomial, near-final draft version (sans bibliography) of Chapter 23 of the Handbook of the Tutte Polynomial and Related Topics, CRC Press, 2022.
T. Chow and J. Paulhus, Algorithmically distinguishing irreducible characters of the symmetric group, Electronic J. Combin. 28 (2021), #P2.5.
T. Chow, The consistency of arithmetic, Math. Intell. 41 (2019), 22–30.
P. Brosnan and T. Chow, Unit interval orders and the dot action on the cohomology of regular semisimple Hessenberg varieties, Advances in Math. 329 (2018), 955–1001. See also the FPSAC 2017 extended abstract and my FPSAC 2017 slides. CORRIGENDUM: In Definition 23 of the full paper, and in Definition 3 of the extended abstract, βi–1 should be replaced with the sum of βj over all j ≤ i–1, and similarly βi should be replaced with the sum of βj over all j ≤ i. I thank John Lentfer for spotting this mistake.
T. Chow, Fair permutations and random k-sets, Problem 11523, Amer. Math. Monthly 117 (October 2010), 741. A solution by Jim Simons was published in the Monthly 119 (November 2012), on pages 801, 802, and 803. My solution, along with my original formulation of the problem, is available here. One open question that I raised was solved by Richard Stanley on MathOverflow. A simpler version of this puzzle appeared on NSA.gov in the January 2017 Puzzle Periodical and was subsequently discussed on the Puzzling StackExchange website. See also Gil Kalai’s Test Your Intuition 56 and its follow-up, as well as Alex Bellos’s Guardian column and its its follow-up.
T. Chow, What Is...a Natural Proof?, Notices AMS 58 (2011), 1586–1587.
T. Chow, Almost-natural proofs, J. Comput. Sys. Sci. 77 (2011), 728–737. Click here for the FOCS 2008 version.
T. Chow and C. K. Fan, The power of multifolds: Folding the algebraic closure of the rational numbers, in Origami4: Proceedings of the Fourth International Conference on Origami in Science, Mathematics, and Education (4OSME), ed. Robert J. Lang, A. K. Peters, 2009, pp. 395–404.
T. Chow, A beginner’s guide to forcing, in Communicating Mathematics, Contemp. Math. 479 (2009), 25–40.
T. Chow, Reduction of Rota’s basis conjecture to a problem on three bases, SIAM J. Discrete Math. 23 (2009), 369–371.
R. J. Chapman, T. Chow, A. Khetan, D. P. Moulton, and R. J. Waters, Simple formulas for lattice paths avoiding certain periodic staircase boundaries, J. Combin. Theory Ser. A 116 (2009), 205–214. CORRIGENDUM: Raney’s paper appeared in Trans. AMS, not Trans. ACM.
T. Chow, T. Kelly, and D. Reeves, Estimating cache hit rates from the miss sequence, Hewlett Packard Technical Report HPL-2007-155, September 2007.
T. Chow, Ein Kleines Schach, Math. Intell. 28 (2006), 49; Solution, page 69.
T. Chow, You could have invented spectral sequences, Notices of the AMS 53(1) (2006), 15–19. CORRIGENDUM (also available on the Notices website)
T. Chow, H. Eriksson, and C. K. Fan, Chess tableaux, Electronic J. Combin. 11(2) (2004–2005), #A3. See also the slides from my MIT Combinatorics Seminar, Chess tableaux and chess problems.
T. Chow and P. J. Lin, The ring grooming problem, Networks 44 (2004), 194–202.
T. Chow, F. Chudak, and A. M. Ffrench, Fast optical layer mesh protection using pre-cross-connected trails, IEEE/ACM Trans. Networking 12 (2004), 539–548.
T. Chow, C. K. Fan, M. X. Goemans, and J. Vondrak, Wide partitions, Latin tableaux, and Rota’s basis conjecture, Advances in Applied Math. 31 (2003), 334–358. See also my slides from Communicating Mathematics, Joseph Gallian’s 65th birthday conference.
T. Chow, Symplectic matroids, independent sets, and signed graphs, Discrete Math. 263 (2003), 35–45. Former titles include “An elementary approach to symplectic matroids” and “An independent set axiomatization of symplectic matroids.”
V. R. Konda and T. Chow, Algorithm for traffic grooming in optical networks to minimize the number of transceivers, Proc. 2001 IEEE Workshop on High Performance Switching and Routing: 29–31 May 2001, Dallas, Texas, 218–221.
T. Chow, Descents, quasi-symmetric functions, Robinson-Schensted for posets, and the chromatic symmetric function, J. Algebraic Combin. 10 (1999), 227–240.
T. Chow and J. West, Forbidden subsequences and Chebyshev polynomials, Discrete Math. 204 (1999), 119–128.
T. Chow, What is a closed-form number? Amer. Math. Monthly 106 (1999), 440–448.
T. Chow and C. Long, Additive partitions and continued fractions, The Ramanujan Journal 3 (1999), 55–72.
T. Chow, The combinatorics behind number-theoretic sieves, Advances in Math. 138 (1998), 293–305.
T. Chow, The surprise examination or unexpected hanging paradox, Amer. Math. Monthly 105 (1998), 41–51. This electronic version includes an extensive bibliography that was omitted from the published version.
T. Chow, The Q-spectrum and spanning trees of tensor products of bipartite graphs, Proc. Amer. Math. Soc., 125 (1997), 3155–3161.
T. Chow, The path-cycle symmetric function of a digraph, Advances in Math. 118 (1996), 71–98.
T. Chow, A short proof of the rook reciprocity theorem, Electronic J. Combin. 3 (1996), R10.
T. Chow, On the Dinitz conjecture and related conjectures, Discrete Math. 145 (1995), 73–82.
T. Chow, Penny-packings with minimal second moments, Combinatorica 15 (1995), 151–158.
T. Chow, Distances forbidden by two-colorings of ℚ3 and An, Discrete Math. 115 (1993), 95–102.
T. Chow, A new characterization of the Fibonacci-free partition, Fibonacci Q. 29 (1991), 174–180.
R. Thibadeau, P. Hsiung, D. Thuel, T. Chow, M. Siegel, An experiment in perfectly realistic graphics, 1989 Annual Research Review, The Robotics Institute, Carnegie Mellon University.
R. Thibadeau, T. Chow, S. Handerson, D. Tin-Nyo, CMU Raytracer, Technical report CMU-RI-TR-88-18, The Robotics Institute, Carnegie Mellon University, 1988.
Slides and script for Pecha Kucha talk at Richard Stanley's 80th birthday conference.
T. Chow, Note on the Schur-expansion of XG for indifference graphs G. Answering a question of Patrick Brosnan, I showed in 2015 that if G is an indifference graph, then the set of partitions λ such that the coefficient of sλ in the Schur-function expansion of XG is nonzero has a unique maximal element in dominance order. My proof uses something I called a “first fit” algorithm. The algorithm has since been rediscovered independently by others, including Fenn and Sommers, and Matherne, Morales, and Selover.
T. Chow, The erasing marks conjecture. This is a conjecture that is related to the Stanley–Stembridge e-positivity conjecture. It also dates back to 2015. I circulated it privately among a few people and then announced it publicly at a Banff workshop in October 2018. The conjecture was proved by Cho, Hong, and Lee.
T. Chow, e-positivity of the coefficient of t in XG(t). Again, I proved this in 2015. John Shareshian tells me that he and Michelle Wachs had previously proved a slightly weaker result than my Corollary 1, but they did not publish their proof either.
T. Chow, Open problem presentation at Stanley’s 70th birthday conference, 2014. This version of the slides contains slightly more information than the version that I actually presented at Stanley@70.
T. Chow, Perfect matching conjectures and their relationship to P ≠ NP, slides from StanleyFest, 2004. NOTE 1: Conjecture 2 in these slides was disproved by Zoltan Kiraly in 2013. In Kiraly’s example, the singleton set consisting of the vertex near the bottom left of the diagram (but not the one on the bottom edge or the left edge of the diagram) is a Tutte set, but no union of parts is a Tutte set. NOTE 2: One of the main motivating questions for this work was whether maximum matchability in graphs is in FP+C. This question was answered affirmatively by Anderson, Dawar, and Holm (LICS 2013).
T. Chow and P. Lin, k-Sperner families, circa 1997 (14 pp). This paper was accepted for publication, but we discovered at the last minute that the results had been superseded by Ruszinkó, “On the upper bound of the size of the r-cover-free families,” J. Combin. Theory Ser. A 66 (1994), 302–310.
T. Chow, A note on a combinatorial interpretation of the e-coefficients of the chromatic symmetric function, 1997 (9 pp).
T. Chow, Symmetric function generalizations of graph polynomials, Ph.D. dissertation, Massachusetts Institute of Technology, 1995 (70 pp).
T. Chow, Spectra and complexity of periodic strips, 1993 (14 pp).
T. Chow, Reconciling alternative definitions of Cohen-Macaulay rings, 1992 (6 pp).
T. Chow, Statistical independence of high range resolution measurements of a moving ground vehicle from diverse aspects, MIT Lincoln Laboratory Project Memorandum 46PM-SSA-0001, February 6, 2003.
T. Chow, Airborne feature-aided tracking of moving ground vehicles across terrain obscurations, MIT Lincoln Laboratory Project Memorandum 46PM-SSA-0002, March 21, 2003.
S. D. Campbell, T. Y. Chow, S. E. Holster, M. A. Weiner, and T. J. Dasey, Urban outdoor biosensor requirements analysis, MIT Lincoln Laboratory Project Report HS-3, May 19, 2006.
V. Sharma, T. Y. Chow, C. E. Rohrs, S. Dunstan, and J. Cerra, Method and apparatus to switch data flows using parallel switch fabrics, U.S. Patents 7123581 and 7859994.
T. Y. Chow, P. J. Lin, and J. D. Mills, Method and system for designing ring-based telecommunications networks, U.S. Patents 7133410 and 7668184.
T. Y. Chow, P. J. Lin, and J. D. Mills, Inter-working mesh telecommunications networks, U.S. Patent 7289428.
T. Y. Chow, F. Chudak, and A. M. Ffrench, Method for allocating protection bandwidth in a telecommunications mesh network, U.S. Patent 7308198.
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