# Publications and Curriculum Vitae

See my c.v. for abstracts; email me (tchow AT alum DOT mit DOT edu) for reprints of papers that are not available below. If the format of the files below gives you trouble, try the Los Alamos 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.

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), 801–803. My solution is available here. One open question that I raised was solved by Richard Stanley on MathOverflow.

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, Is perfect matchability of unordered graphs in fixed-point logic with counting? in preparation. In the meantime, you can look at the slides from my talk at StanleyFest, Perfect matching conjectures and their relationship to PNP. NOTE: 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.

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. ERRATUM: 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. ERRATUM: Thanks to Stuart Ambler for noticing that in Claim 2 on page 17, E1d,2 should be E1d+1,2.

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 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.

## Unpublished manuscripts

T. Chow, Symmetric function generalizations of graph polynomials, Ph.D. dissertation, Massachusetts Institute of Technology, 1995 (70 pp).

T. Chow, Reconciling alternative definitions of Cohen-Macaulay rings, 1992 (6 pp).

T. Chow, Spectra and complexity of periodic strips, 1993 (14 pp).

## Lincoln Laboratory papers

Obtaining a copy of these papers requires prior written approval from MIT Lincoln Laboratory. Contact me for details.

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.

## Patents

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.