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 A well-motivated proof that pi is irrational, preprint.

T. Chow Cooking poisons: thinking laterally with game theory,
*Mathematics
Magazine*, to appear.

L. Barnes, T. Chow, E. Cohen, K. Frankston, B. Howard, F. Kochman, D. Scheinerman, and J. VanderKam, Efficient unbiased sparsification, ISIT 2024, WE2.R2.4.

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.

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 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 and C. K. Fan,
The power of multifolds:
Folding the algebraic closure of the rational numbers,
in *Origami*^{4}: 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
ℚ^{3}
and *A _{n}*,
Discrete Math.

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 *X _{G}* for indifference graphs

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 *X _{G}*(

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.