Transparencies

If you have trouble downloading any of the files or would prefer a hard copy, please e-mail me at: rstan (at math.mit.edu)

Enumeration of solutions to equations in finite groups (26 pages)
Université du Québec à Montréal (UQAM), June 1997
The distance enumerator of a hyperplane arrangement (41 pages)
Tokyo Metropolitan University, 15 July 1998
The Whitehouse module (32 pages)
RIMS, Kyoto University, 21 July 1998
Otto-von-Guericke-Universität Magdeburg, 11 August 1998
Log-concave and unimodal sequences in algebra, combinatorics, and geometry (34 pages)
Michigan State University, 6 October 1998
The characteristic polynomial of a hyperplane arrangement (41 pages)
Michigan State University, 7 October 1998
Georgia Institute of Technology, 26 May 1999
U.C. Berkeley, 1 November 2004
Parking functions (35 pages) (slightly modified 1/4/99)
Michigan State University, 9 October 1998
Hebrew University, 20 January 1999
version for MIT Math Club, 4 May 2004
version for NSA, 16 September 2011
version for University of Pennsylvania, 11 November 2015
version for University of Southern California, 27 November 2018
version for Stanford University, January 2020
Volumes of convex polytopes (48 pages)
Bar-Ilan University, 10 January 1999
Hebrew University, 18 January 1999
Otto-von-Guericke-Universität Magdeburg, 22 January 1999
Spanning trees (31 pages)
Bar-Ilan University, 10 January 1999
Hebrew University, 14 January 1999
Volumes and Ehrhart polynomials of convex polytopes (39 pages)
Georgia Institute of Technology, 27 May 1999
Hyperplane arrangements and interval orders (20 pages)
Northeastern University, 15 June 1999
Mathematical games (pdf) (46 pages)
M.I.T., 22 June 1999
M.I.T., 25 January 2002
M.I.T., 14 January 2008 (slightly expanded)
M.I.T., 21 January 2011 (improved and expanded)
Problems and conjectures on f-vectors (25 pages)
Osaka University, 27 July 1999
Generalized riffle shuffles and quasisymmetric functions (18 pages)
Providence, RI, 2 October 1999
Université du Québec à Montréal (UQAM), 29 October 1999
Chess and mathematics (PostScript or pdf) (27 pages): the second lecture in a series of two lectures (the first given by Noam Elkies) based on a book in preparation. Excerpt from book: 12 page PostScript or PDF file.
M.I.T., 13 January 2000
Acyclic flow polytopes and Kostant's partition function (12 pages)
Washington, DC, 22 January 2000

Expanded version (latest revision 8/30/00, 29 pages)
U.C. Berkeley, 20 March 2000
Stanford University, 22 March 2000
AT&T Laboratories, 21 July 2000
Université du Québec à Montréal (UQAM), 9 September 2000
Some open problems in enumerative combinatorics (31 pages)
Foatafest, Temple University, 7 July 2000
Recent progress in algebraic combinatorics : (1) the Saturation Conjecture, (2) the n! and (n+1)^n-1 conjectures, (3) longest increasing subsequences (52 pages)
UCLA, 7 August 2000
Polynomials with real zeros (36 pages)
University of Kentucky, 6 March 2001
Texas A&M University, 24 March 2001
The mathematical legacy of Rodica Simion (30 pages)
FPSAC, Arizona State University, 22 May 2001
Border strips, snakes and codes of skew partitions (30 pages)
M.I.T., 19 September 2001
University of Michigan, 29 March 2002
IDA-CCR, Princeton, 8 April 2002
KTH, 21 May 2002
Free probability for combinatorialists (pdf) (23 pages)
Williamstown, MA, 13 October 2001
A survey of flag f-vectors and flag h-vectors I (25 pages)
University College London, 18 May 2002 (Part II was given by Louis Billera.)
Kerov's character polynomial and irreducible symmetric group characters of rectangular shape (16 pages)
Québec City, June 2002
Open problems related to chromatic symmetric functions (31 pages)
Mount Holyoke College, 21 July 2002
A survey of generating functions (58 pages)
New Plymouth, New Zealand, 7-8 January 2003
Recent progress in algebraic combinatorics: (1) the Laurent phenomenon, (2) toric Schur functions, (3) sign imbalance (47 pages)
FPSAC, Vadstena, Sweden, 25 June 2003
U. C. Davis, 21 January 2004
open problem (three pages) presented at FPSAC (later solved by M. Ishikawa, math.CO/0408204)
A survey of the Bruhat order of the symmetric group (PDF) (37 pages)
CCR-P, Princeton, NJ, 29 June 2003 (postponed to 8 August 2003)
version for Nankai University, 4 August 2004 (31 pages)
A survey of lattice points in polytopes (37 pages)
Stockholm, 24 October 2003
UCSD, 26 January 2004
Enhanced version, ECNU, Shanghai, 21 July 2009
MIT Undergraduate Mathematics Association version, 14 February 2012
Slightly expanded version Harbin Institute of Technology, 7 August 2012
Inaugural Conference of the Institute of the Mathematical Sciences of the Americas, Miami, 8 September 2019
version for Stanford University, January 2020
Schubert polynomials and chains in the Bruhat order of the symmetric group (14 pages)
Phoenix, 7 January 2004
Extended version presented at M.I.T., 28 April 2004 (22 pages)
Recent developments in algebraic combinatorics: (1) toric Schur functions, (2) toric h-vectors and intersection cohomology (30 pages)
Yale University, 30 March 2004
Some problems I couldn't solve (15 pages)
M.I.T., 26 June 2004
Update
Tilings (PDF, slightly corrected version of 10 November 2005) (57 pages)
Clay Public Lecture, Park City, Utah, 16 July 2004
Version (somewhat more mathematical), IAP lecture, M.I.T., 19 January 2007
Version (better graphics), Sulski Lecture, College of the Holy Cross, Worcester, MA, 24 April 2007
Hyperplane arrangements and special relativity (30 pages)
MSRI, 4 November 2004
Linköping, Sweden, 4 April 2005
Crossings and nestings of matchings and partitions (26 pages)
Montreal, 13 December 2004
The RSK algorithm and its applications (three lectures) (53 pages)
University of Haifa, 21-23 March 2005
An introduction to RSK (29 pages)
Netzeband, Germany, 3 June 2005
Increasing and decreasing subsequences
Original version (36 pages): Colonia, Uruguay, 2 August 2005
Expanded version (45 pages): WPI, 10 September 2005
Two-lecture version (56 pages): Texas A&M University, October 2005 (corrected and updated 14 October 2005)
Another version (43 pages): UCSD, 8 December 2005, and Arizona State University, 18 January 2006
Version: Drexel University, 21 April 2009
Version: University of Rome, May 2009
Version: University of Southern California, 26 November 2018
Standard Young tableaux (23 pages)
Texas A&M, October 2005
Open problem on F(-F(-x)) = x (3 pages)
San Antonio, 14 January 2006
A conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group (14 pages)
Storrs, CT, 27 October 2006
Alternating permutations (28 pages)
Montreal, 28 March 2007
Version: University of Kentucky, 28 March 2009
Version: IPM, Tehran, Iran, May 2009
Version: University of Connecticut, 15 April 2010
Version: SIAM Conference on Discrete Mathematics, Austin, TX, 17 June 2010
Version: IDA, Princeton, NJ, 5 August 2010
Promotion and evacuation (36 pages); pdf
Stockholm, 30 May 2008
Partition statistics with respect to Plancherel measure (26 pages); pdf
Cornell, 14 June 2008
Version entitled Hooks and contents, Penn State, 5 December 2008
The Erdös-Moser conjecture
University of Kentucky, 29 March 2009
Hyperplane arrangments and combinatorics (three instructional lectures)
Sapporo, 2-4 August 2009
Recent work on special polytopes
IPAM, UCLA, 23 October 2009
AMS Colloquium Lectures, January 13-15, 2010: Increasing and decreasing subsequences, Alternating permutations, Reduced decompositions .
Clifford Lectures, Tulane University, March 25-27, 2010. Three lectures on lattice points in polytopes: #1 , #2 , #3
Products of cycles
Permutation Patterns 2010, Dartmouth College, August 2010
Version for Waterloo Workshop on Computer Algebra, May, 2011
A chromatic symmetric function conjecture
Special Session on My Favorite Graph Theory Conjectures, AMS Winter Meeting, Boston, 7 January 2012
The visibility arrangement and line shelling arrangment of a convex polytope
Workshop on Convex Polytopes, Kyoto, Japan, 25 July 2012
Version: 11th Nordic Combinatorial Conference, 17 June 2013
Version: 2013 Combinatorics Workshop, NIMS, Daejeon, Korea, 9 August 2013
Polynomial sequences of binomial type
2012 Shanghai Conference on Algebraic Combinatorics, 18 August 2012
University of Miami, 15 January 2013
Two enumerative tidbits
The Combinatorics of q-Series and Partitions, Nankai University, August 2-4, 2013, and NIMS Hot Topics 2013 Combinatorics Workshop, Daejeon, August 7-9, 2013 (The two tidbits are "The Smith normal form of some matrices connected with Young diagrams" and "A distributive lattice associated with three-term arithmetic progressions"
Magic squares and syzygies
500 Years of Melancolia in Mathematics, NYU Polytechnic School of Engineering, May 17, 2014 ("general audience" talk). Revised for public lecture in honor of Nicolas del Castillo, Universidad de los Andes, Bogotá, 6 June 2014.
Wishful thinking as a proof technique,
M.I.T., 27 June 2014
Some Catalan musings
DIMACS Conference on Challenges of Identifying Integer Sequences, 9 October 2014
Version for IMA Workshop on Geometric and Enumerative Combinatorics, 11 November 2014.
version for University of Miami lecture series, spring 2020
version for REU at New York University (via Zoom), 19 July 2021
Smith normal form and combinatorics
Princeton University, 10 April 2015
version for the conference "Ira Gessel 2015" at Brandeis University
version for AMS Special Session on Algebraic and Topological Methods in Combinatorics, Seattle, 8 January 2016
version for the conference Number Theory in honor of Krishna Alladi's 60th birthday, Gainesville, 20 March 2016
version for various Japanese universities, 2017
version Stanford University, January 2020
Catalan numbers (for undergraduates)
Chongqing University, 13 June 2016
Sichuan University , 20 June 2016
version for Tsuda University, 10 July 2017
version for Tulane University, 22 March 2018
version for Math 225, Wellesley College (via Zoom), 13 March 2024
Plethysm and Kronecker products
Bowdoin College, 24 September 2016
Some aspects of (r,k)-parking functions (with Yinghui Wang (王颖慧))
Bowdoin College, 24 September 2016
Stern's diatomic array and beyond
M.I.T., 19 September 2018
LACIM (Montreal), 25 September 2018
version for Center for Applied Mathematics, Tianjin, October, 2019.
version for Rutgers University (Zoom talk), 19 November 2020
I. Stern's diatomic array and beyond. II. Spernicity of the weak order on S_n
Sergey Fomin 60th birthday conference, Ann Arbor, 11 November 2018
University of Southern California, 28 November 2018
Stanford University, 31 January 2019
The Sperner property, University of California at Irvine, 24 January 2019
Version for Garsiafest, San Diego, 17 June 2019
Persification, Talking Across Fields, Stanford University, 2 February 2020
(n+1)^n-1 , part of Lecture Series, University of Miami, spring 2020 (April 7)
Video (available only to those with a U. Miami account)
(2n-1)!! , part of Lecture Series, University of Miami, spring 2020 (April 14)
Video (available only to those with a U. Miami account)
From Stern's triangle to upper homogeneous posets , Institut Mittag-Leffler Algebraic Combinatorics Online Workshop (ACOW), 20 April 2020. Note. The conjecture on page 32 has been proved by Arthur L. B. Yang.
Two analogues of Pascal's triangle, Combinatorics and Graph Theory Seminar, Michigan State University, 3 February 2021 (via Zoom)
Slight variant for University of North Carolina at Greensboro, 10 March 2021, and University of Massachusetts at Amherst, 12 March 2021 (via Zoom)
Version for Conference on the Occasion of the Retirement of Yeong-Nan Yeh, June 27-28, 2021 (via Zoom)
Version for KTH, Stockholm, October 6, 2021 (via Zoom)
Version for Beijing Institute of Technology, October 13, 2024
Chains and antichains: first part of lecture series to graduate students at University of Miami, spring semester, 2021
Two poset polytopes: second part of lecture series to graduate students at University of Miami, spring semester, 2021
Order polynomials: third part of lecture series to graduate students at University of Miami, spring semester, 2021
A survey of unimodality and log-concavity: Zoom talk for P-positivity in Matroid Theory and Related Topics, October 3-8, 2021, RIMS, Kyoto, Japan
A Fibonacci analogue of Pascal's triangle: Zoom talk for Reflections: On the occasion of Ron Adin's and Yuval Roichman's 60th birthdays, Bar-Ilan University, 10 January 2022
Permutation enumeration and symmetric functions: Zoom talk for FPSAC'21, Bar-Ilan University, 20 January 2022
The X-Descent Set of a Permutation, Combinatorial and Algebraic Enumeration, Waterloo, Ontario, 26 May 2022
version for Algorithmic and Enumerative Combinatorics, Vienna, 4 July 2022
version (corrected) for International Conference on Enumerative Combinatorics and Applications (ICECA 2022), virtual, 6 September 2022
Version for WYSS 2022-Forum on Mathematics and Its Applications, Wenzhou, virtual, 21 October 2022
Two Analogues of Pascal's Triangle, Number Theory Seminar, University of Florida, 4 April 2023
Euler Numbers, 14th Ramanujan Colloquium, University of Florida, Gainesville, 3 April 2023
Some of My Favorite Posets, ICECA, 4 September 2023
A Fibonacci Array (six-minute talk aimed at "recreational mathematicians"), Gathering 4 Gardner, Atlanta, 22 February 2024
Some Combinatorial Aspects of Cyclotomic Polynomials, Conference on Enumerative and Algebraic Combinatorics in honor of Bruce Sagan, University of Florida, Gainesville, 26 February 2024.
Expanded version (with modified title "Some Enumerative Aspects of Cyclotomic Polynomials"), Combinatorics Seminar, University of Miami, 1 April 2024.
Version for ICECA 2024, 26 August 2024.
Generating Functions I Have Known, The Many Combinatorial Legacies of Richard P. Stanley, Harvard University, 7 June 2024

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