Welcome to Tom Roby's Research Page!
My primary research interests are (1) algebraic and enumerative combinatorics,
particularly connections with permutations, tableaux, and representation
theory; and (2) mathematics education, particularly outreach to K12
teachers and support for K16 learners.
Mathematics Publications and Preprints:
 Iterative properties of
birational rowmotion (I & II)
(with D. Grinberg), submitted for
publication as two papers.
 Homomesy in products of two chains
(with J. Propp), submitted and undergoing secondary revisions.
Extended Abstract published in Disc. Math. &
Theoretical Comp. Sci. Proceedings, 25nd International Conference on
Formal Power Series and Algebraic Combinatorics (FPSAC 2013).
 Equivalence Classes of
Permutations under Various Relations Generated by Constrained
Transpositions (with S. Linton, J. Propp,
J. West), Journal of
Integer Sequences 15
(2012), Article 12.9.1. Earlier preprint
is arXiv:1111.3920
[math.CO].
 Equivalence Relations of Permutations Generated by Constrained Transpositions
(with S. Linton, J. Propp, J. West), Disc. Math. &
Theoretical Comp. Sci. Proceedings, 22nd International Conference on
Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010.
 A twodimensional pictorial
presentation of Berele's insertion algorithm
for symplectic tableaux (with I. Terada).
Electronic Journal of Combinatorics, Volume 12(1), 2005, R4.
 The Lattice of Threshold Graphs (with Russ Merris),
J. Ineq. Pure & Appl. Math (JIPAM)
vol. 6, #1 (2005)
 A Schensted insertion for tensor
powers of the Weil representation, accepted as a poster at FPSAC
2002, Melbourne.
 Complementary Algorithms for Tableaux (with
Frank Sottile, Jeff Stroomer, and
Julian West). Journal of Combinatorial TheoryA 96, 127161 (2001).
Available in postscript or tarred and gzipped
.
 Jeux de
tableaux (With F. Sottile, J. Stroomer, J. West). Formal Power Series
and Algebraic Combinatorics: Twelfth International Conference, FPSAC'00,
Moscow, Russia, June 2000, Proceedings, pp. 332343.

Downup Algebras (with Georgia Benkart) Journal of Algebra 209
, 35344 (1998) A brief addendum is
available.
 The connection between the RobinsonSchensted
correspondence for skew oscillating tableaux and graded graphs.
Discrete Math. 139 (1995) 481485.
 Applications and Extensions of Fomin's
Generalization of the RobinsonSchensted Correspondence to Differential
Posets, Ph.D. Thesis, Massachusetts Institute of Technology,
1991. Here's a PDF scan of this.
Slides from talks (reverse chronologically):
NB: The animations (by Mike LaCroix) in several of the presentations below run (only?) in
versions of adobe acrobat (reader), not in preview, but summary slides
viewable in other readers are included for each animation.
 Birational Rowmotion: order, homomesy, and cluster
connections
given in the
Combinatorics Seminar,
at University of Minnesota, 22 May
2015.
 Birational Rowmotion given
at (the NSF cosponsored)
Dynamical Algebraic Combinatorics Workshop at
American Institute of Mathematics, San Jose, CA, 24 March
2015.
 SeeSaw Swap Solitaire and
Other Games on Permutations given
at Canada/USA Mathcamp, Lewis & Clark, Portland, OR, 29 July 2014.
 Rowmotion: Classical \& Birational given
at Stanley@70
Conference, MIT, Cambridge, MA, 26 June 2014.
 The Eleven Clocks Problem given
at Gathering for
Gardner XI, Atlanta, GA, 22 March 2014.
 Homomesy of Order
Ideals in Products of Two Chains
given in the
Combinatorics Seminar,
at University of Minnesota, 6 Sept
2013.
 (with Darij
Grinberg) Combinatorial
Actions,
Orbit Averages, and Sage Implementation
given at Sage Days
49, 18 June 2013.
 Combinatorial
Actions and Homomesic Orbit Averages
given in the
Mathematics
Colloquium,
at Dartmouth College, 23
May 2013.
 Homomesy of Order
Ideals in Products of Two Chains
given in the
Combinatorics Seminar,
at Dartmouth College, 23
May 2013.
 Combinatorial Ergodicity
given in the
Algebra seminar,
at the University of
Connecticut, 27 March 2013.
 Combinatorial Ergodicity
given
in the Workshop on
Algebraic Combinatorics related to Young diagrams and Statistical
Physics, at the International
Institute for Advanced Study in Kizugawashi, Kyoto,
Japan, 9 August 2012.
 Combinatorial Ergodicity
given at the University of Tokyo,
Department of Mathematical Sciences, Tokyo, Japan, 23 July 2012.
 Combinatorial Ergodicity in
Products of Chains
given at SIAM
Discrete Math 2012 Conference at Dalhausie University, Halifax, NS,
Canada, 18 June 2012.
 SeeSaw Swap
Solitaire given
at Gathering for
Gardner X, Atlanta, GA, 29 March 2012.
 A Bijection that Counts: The
RobinsonSchenstedKnuth Correspondence at Joint Math Meetings, 5
January 2012.
 Equivalences relations
of permutations generated by constrained transpositions in MIT
Combinatorics Seminar, 18 November 2011.
 More history to appear eventually...!
Math Education Publications and Preprints:
 More recent texts to appear soon...
 (with Maletsky, E. and seven other authors) Harcourt
Math (Grades K6) Harcourt, Inc., Orlando, 2004.
 "Models for fractions" in Harcourt Math Professional
Handbook (Orlando, 2002), pp. PH2425.
 The JOMA mathlets project. Journal
of Online Mathematics and its Applications 1 (Jan, 2001).
