Sergi Elizalde

Phone:

(603) 6468191

Dept.
Fax:

(603) 6461312

Office:

332 Kemeny Hall

Office Hours:

Tu 910:30,
Fr 11:0512:30

Email:


US Mail:

Department of
Mathematics
6188 Kemeny Hall
Dartmouth College
Hanover, NH 037553551

I am an Associate Professor in the Department of Mathematics at Dartmouth College.
My research interests are mostly in enumerative and algebraic combinatorics. I have worked on permutations, patterns, bijections, triangulations, lattice paths, generating
functions, algorithms, number theory, and applications of combinatorics
to computational biology and dynamical systems.
Here you can download my CV and publication
list with abstracts. Before coming to Dartmouth, I was at MIT as a
grad student of Richard Stanley, and at MSRI as a postdoc. Before
that I was a student at UPC in Barcelona.
I am coorganizing the Discrete Math
Day conference on April 12 at Dartmouth. Check out the poster here.
Spring 2014 teaching:
·
Math 38.
Graph Theory.
Current Ph.D. students
·
Kassie Archer
·
Jonathan
Bloom
·
Megan Martinez
·
Tim Dwyer
I coorganized the conference Permutation Patterns 2010.
The proceedings have been published in a special issue of Pure Mathematics and Applications.
Recent
Preprints
 Symmetries of statistics on lattice paths
between two boundaries (with M. Rubey), preprint, arXiv:1305.2206.
 A generating tree approach to knonnesting partitions and permutations (with M. Mishna,
S. Burrill and L. Yen), preprint, arXiv:1108.5615.
Journal Publications
 Cyclic permutations realized by signed shifts
(with K.
Archer), J. Comb. 5
(2014), 1—30. arXiv:1304.7790.
 Inversion polynomials for
321avoiding permutations (with S.E. Cheng,
A. Kasraoui and B. Sagan), Discrete Math. 313 (2013),
25522565. arXiv:1112.6014.
 Arc permutations (with Y. Roichman),
J. Algebraic Combin.
39 (2014), 301—334. arXiv:1210.6056.
 Total occurrence statistics on restricted
permutations (with A.
Burstein), Pure Math. Appl. (PU.M.A.), to
appear. arXiv:1305.3177.
 Pattern avoidance in matchings
and partitions (with J. Bloom), Electron. J. Combin.
20 (2013), #P5. arXiv:1211.3442.
 The most and the least avoided consecutive
patterns, Proc. Lond.
Math. Soc. 106 (2013), 957—979, doi: 10.1112/plms/pds063.
arXiv:1203.1636.
 Clusters, generating functions and asymptotics for consecutive patterns in permutations
(with M. Noy), Adv. in Appl. Math. 49 (2012), 351–374. arXiv:1210.6061.
 Fixed points and excedances in restricted permutations, Electron. J. Combin.
18 (2012), #P29.
 Permutations and βshifts, J. Combin. Theory Ser. A 118 (2011), 24742497. arXiv:1008.4167.
 Descent sets of cyclic permutations, Adv.
in Appl. Math. 47 (2011), 688709. arXiv:0906.2795.
 Restricted simsun
permutations (with E. Deutsch), Ann. Comb. 16 (2012), 253–269. arXiv:0912.1361.
 On basic forbidden patterns of functions
(with Y. Liu), Discrete Appl. Math 159 (2011), 12071216. arXiv:0909.2277.
 Cycleupdown permutations (with E. Deutsch),
Australas. J. Combin.
50 (2011), 187199. arXiv:0909.5199.
 The Xclass and
almostincreasing permutations, Ann. Comb. 15 (2011), 5168. arXiv:0710.5168.
 Improved bounds on the number of numerical semigroups of a given genus, J. Pure Appl. Algebra
214 (2010), 18621873. arXiv:0905.0489.
 The largest and the smallest fixed points of
permutations (with E. Deutsch), European J. Combin.
31 (2010), 14041409. arXiv:0904.2792.
 The number of permutations
realized by a shift, SIAM J. Discrete Math. 23 (2009), 765786. arXiv:0909.2274.
 Forbidden patterns and shift
systems (with J.M. Amigó and M.B. Kennel), J.
Combin. Theory Ser. A 115 (2008), 485504. arXiv:0707.4628.
 Generating trees for
permutations avoiding generalized patterns, Ann. Comb. 11 (2007),
435458. arXiv:0707.4633.
 A bijection
between 2triangulations and pairs of noncrossing Dyck
paths, J. Combin. Theory Ser. A 114/8 (2007),
14811503. arxiv:math.CO/0610235.
 Bounds on the number of
inference functions of a graphical model (with K. Woods), Statist. Sinica 17 (2007), 13951415, arxiv:math.CO/0610233.
 The probability of choosing
primitive sets (with K. Woods), J.
Number Theory 125 (2007), 3949, arxiv:math.NT/0607390.
 Restricted Dumont
permutations, Dyck paths, and noncrossing partitions (with A. Burstein and T. Mansour), Discrete Math.
306 (2006), 28512869, arXiv:math/0610234.
 Combinatňria i biologia:
funcions d'inferčncia
i alineació de seqüčncies,
Butl. Soc. Catalana Mat. 21
(2006), n. 1, 39–52. [Download]
 Asymptotic enumeration of
permutations avoiding generalized patterns, Adv. in Appl. Math. 36
(2006), 138155, arXiv:math/0505254.
 Old and young leaves on plane
trees (with W.C. Chen and Emeric
Deutsch), European J. Combin. 27 (2006),
414427, arXiv:math/0410127.
 Multiple patternavoidance
with respect to fixed points and excedances, Electron.
J. Combin. 11 (2004), #R51, arXiv:math/0311211.
 Restricted Motzkin
permutations, Motzkin paths, continued
fractions, and Chebyshev polynomials (with T. Mansour), Discrete Math.
305 (2005), 17018, arXiv:math/0610237.
 A simple and unusual bijection for Dyck paths and
its consequences (with E. Deutsch), Ann. Comb. 7 (2003), 281297, arXiv:math/0306125.
 Bijections
for refined restricted permutations (with I. Pak), J. Combin. Theory Ser. A 105 (2004), 207219, arXiv:math/0212328.
 Consecutive patterns in
permutations (with M. Noy), Adv. in Appl. Math. 30 (2003), 110125. [Download]
Book Chapters
 Inference functions, chapter of the book Algebraic Statistics for
Computational Biology, edited by L. Pachter
and B. Sturmfels,
Cambridge University Press, 2005.
 Bounds for optimal sequence alignment (with F. Lam), chapter of the
book Algebraic
Statistics for Computational Biology, edited by L. Pachter
and B. Sturmfels,
Cambridge University Press, 2005.
Refereed Conference Proceedings
 Periodic
patterns of signed shifts (with K. Archer), Discrete
Math. Theor. Comput.
Sci. proc. AS (2013), 873884. [Download
extended abstract].
 Patterns in matchings
and rook placements (with J. Bloom), Discrete Math. Theor.
Comput. Sci. proc. AS (2013), 909920.
 Bijections for lattice
paths between two boundaries (with M. Rubey), Proceedings of FPSAC 2012, Discrete Math. Theor.
Comput. Sci. proc. AR (2012), 827838.
 Arc Permutations (extended abstract) (with Y. Roichman), Proceedings of FPSAC 2012, Discrete Math. Theor.
Comput. Sci. proc. AR (2012), 259270.
 Consecutive patterns in permutations: clusters
and generating functions (with M. Noy), Proceedings
of FPSAC 2012, Discrete Math. Theor. Comput. Sci. proc. AR
(2012), 247258.
 Generating trees for partitions and permutations
with no knestings (with M.
Mishna, S.
Burrill and L. Yen),
Proceedings of FPSAC 2012, Discrete
Math. Theor. Comput.
Sci. proc. AR (2012), 409420.
 Allowed patterns of betashifts, Proceedings of FPSAC 2011, Discrete
Math. Theor. Comput.
Sci. proc. AO (2011), 293304.
 Sorting by Placement and Shift (with P. Winkler), Proceedings
of the Twentieth Annual ACMSIAM Symposium on Discrete Algorithms, SODA
2009, arXiv:0809.2957.
 Permutations realized by shifts, Proceedings of FPSAC 2009, Discrete
Math. Theor. Comput.
Sci. proc. AK (2009), 361372.
 Pattern avoidance in dynamical systems (with J.M.
Amigó, M.B. Kennel), Proceedings of FPSAC 2008, Discrete Math. Theor.
Comput. Sci. proc. AJ (2008), 7182.
 A bijection between
2triangulations and pairs of noncrossing Dyck
paths, Proceedings of FPSAC 2007.
 Bounds on the number of inference functions of a
graphical model (with K. Woods), Proceedings of FPSAC 2006.
 Old and young leaves on plane and binary trees (with E. Deutsch), Proceedings of FPSAC 2005.
 Restricted Motzkin
permutations (with T. Mansour), Proceedings of FPSAC 2004.
 Fixed points and excedances
in restricted permutations, Proceedings of FPSAC 2003, arxiv:math.CO/0212221.
 Forbidden subwords in
permutations (with M. Noy), Proceedings
of FPSAC 2001.
Unpublished material
·
An
involution on lattice paths between two boundaries. [Download]
·
My MIT Ph.D.
Thesis: Statistics on Patternavoiding Permutations, Ph.D. thesis, MIT,
2004. [Download pdf,
ps]
Some slides of talks I have given
 Consecutive patterns in
permutations [Plenary
talk at Permutation Patterns 2013].
 Bijections
for lattice paths between two boundaries [SIAM
DM'12, CanaDAM 2013].
 Consecutive patterns in
permutations: clusters, generating functions, and asymptotics
[Slides
Feb 2012]
 Allowed patterns of βshifts [FPSAC
2011 Slides]. Permutations
and βshifts [Slides
Oct 2010]
 The number of numerical semigroups of a given genus. [Slides
Jun 2010]
 Descent sets of cyclic
permutations. [Slides
Oct 2009, Slides
Apr 2010]
 Sorting by placement and
shift [Slides
Jan 2009]. A greedy sorting algorithm [Slides
Feb 2010]
 Discrete
Mathematics Day, Middlebury College, September 2007, Forbidden patterns in telling random from
deterministic time series. [Slides]
 MIT Combinatorics Seminar,
September 2006, A bijection between 2triangulations
and pairs of noncrossing Dyck paths. [Slides]
 International
Conference on Permutation Patterns, PP'06, Reykjavik, Iceland, June
2006, Generating trees for permutations avoiding generalized patterns.
[Slides]
 Institut MittagLeffler
Seminar, Djursholm, Sweden, May 2005, Combinatorics
from biology: inference functions and sequence alignment. [Slides]
 International
Conference on Permutation Patterns, PP'05, Gainesville, Florida, March
2005, Asymptotic enumeration of
permutations avoiding generalized patterns. [Slides]
 MIT Combinatorics Seminar,
February 2005. Inference functions and sequence alignment. [Slides]
 Stanford
University Representation Theory Seminar, December 2004, Refined enumeration of patternavoiding
permutations. [Slides]
 International Conference on Permutation
Patterns, PP'04, Nanaimo, Canada, July 2004, Simultaneous
patternavoidance with respect to fixed points and excedances.
[Slides]
 Thesis defense, MIT, April
2004, Statistics on Patternavoiding Permutations. [Slides]
 UC Berkeley
Combinatorics Seminar, February 2004, Refined
enumeration of patternavoiding permutations. [Slides]
 MIT Combinatorics Seminar,
November 2003. Patternavoiding permutations: old results and new
developments. [Slides]
 FPSAC 2003, Vadstena,
Sweden, June 2003. Fixed points and excedances
in restricted permutations. [Slides]
 MIT Simple Person's Applied
Math Seminar, November 2002. What pattern avoidance shouldn't have
avoided. [Slides]
Past teaching
Links
 Richard
Stanley's 70th birthday conference, MIT, June 2327, 2014.
 Permutation Patterns 2010 at Dartmouth,
August 913, 2010.
 Discrete Mathematics Day at
Dartmouth, October 2007.
 Discrete Math Days
permanent website.