Transparencies
If you have trouble downloading any of the files or would prefer a
hard copy, please email 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
OttovonGuerickeUniversität Magdeburg, 11 August 1998

Logconcave 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)
BarIlan University, 10 January 1999
Hebrew University, 18 January 1999
OttovonGuerickeUniversität Magdeburg, 22 January 1999

Spanning trees (31 pages)
BarIlan 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 fvectors (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)^{n1}
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
IDACCR, Princeton, 8 April 2002
KTH, 21 May 2002
 Free probability for
combinatorialists (pdf)
(23 pages)
Williamstown, MA, 13 October 2001
 A survey of flag fvectors
and flag hvectors 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, 78 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)
CCRP, 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 hvectors 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
 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
Twolecture 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 ErdösMoser
conjecture
University of Kentucky, 29 March 2009
 Hyperplane arrangments and
combinatorics (three instructional lectures)
Sapporo, 24 August 2009
 Recent work on special
polytopes
IPAM, UCLA, 23 October 2009
 AMS Colloquium Lectures, January 1315, 2010:
Increasing and decreasing
subsequences, Alternating permutations,
Reduced decompositions.
 Clifford Lectures, Tulane University, March 2527, 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 qSeries and Partitions, Nankai
University, August 24, 2013, and NIMS Hot Topics 2013 Combinatorics
Workshop, Daejeon, August 79, 2013 (The two tidbits are "The Smith
normal form of some matrices connected with Young diagrams" and "A
distributive lattice associated with threeterm 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
 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
 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)^{n1} ,
part of Lecture Series, University of Miami, spring 2020 (April 7)
Video
(available only to those with a U. Miami account)
 (2n1)!! ,
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 MittagLeffler 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
 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
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