Sergi Elizalde

	Phone:	(603) 646-8191
	Dept. Fax:	(603) 646-1312
	Office:	332 Kemeny Hall
	Office Hours:	By appointment
	Email:
	US Mail:	Department of Mathematics 6188 Kemeny Hall Dartmouth College Hanover, NH 03755-3551

Welcome to my homepage!

I am an Assistant Professor in the Department of Mathematics at Dartmouth College.

I completed my Ph.D. at MIT in 2004 under the supervision of Richard Stanley. Afterwards I was a Postdoctoral Fellow at MSRI, and later a John Wesley Young instructor at Dartmouth.

My research interests are in enumerative and algebraic combinatorics. I have worked on pattern-avoiding permutations, bijections, generalized triangulations, lattice paths, generating functions, algorithms, number theory, and applications to computational biology and dynamical systems.

Here you can download my CV, research statement and publications with abstracts.

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Past teaching

• Fall 2009: Math 81. Abstract Algebra.
• Fall 2008: Math 3. Introduction to Calculus; Math 101. Topics in Algebra.
• Winter 2008: Math 108. Topics in Combinatorics: The probabilistic method.
• Fall 2007: Math 68. Algebraic Combinatorics.
• Spring 2006: Math 38. Graph Theory.
• Fall 2006: Math 108. Topics in Combinatorics; Math 11. Multivariable Calculus.
• Summer 2006: Math 20. Discrete Probability.
• Spring 2006: Math 16. Linear Programming; Math 38. Graph Theory.
• Fall 2005: Math 68. Algebraic Combinatorics; Math 3. Introduction to Calculus.

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List of publications and preprints.

1. On basic forbidden patterns of functions (with Y. Liu), preprint, arXiv:0909.2277.
   
   
2. Descent sets of cyclic permutations, preprint, arXiv:0906.2795.
   
   
3. Improved bounds on the number of numerical semigroups of a given genus, preprint, arXiv:0905.0489.
   
   
4. The largest and the smallest fixed points of permutations (with E. Deutsch), European Journal of Combinatorics, to appear, arXiv:0904.2792.
   
   
5. The number of permutations realized by a shift, SIAM J. Discrete Math. 23 (2009), 765-786. arXiv:0909.2274.
   
   
6. Sorting by Placement and Shift (with P. Winkler), Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2009, arXiv:0809.2957.
   
   
7. The X-class and almost-increasing permutations, Annals of Combinatorics, to appear, arXiv:0710.5168.
   
   
8. Forbidden patterns and shift systems (with J.M. Amigó and M.B. Kennel), Journal of Combinatorial Theory - Series A 115 (2008), 485-504, arXiv:0707.4628.
   
   
9. Generating trees for permutations avoiding generalized patterns, Annals of Combinatorics 11 (2007), 435-458, arXiv:0707.4633.
   
   
10. A bijection between 2-triangulations and pairs of non-crossing Dyck paths, Journal of Combinatorial Theory - Series A 114/8 (2007), 1481-1503, arxiv:math.CO/0610235.
    
    
11. Bounds on the number of inference functions of a graphical model (with K. Woods), Statistica Sinica 17 (2007), 1395--1415, arxiv:math.CO/0610233.
    
    
12. The probability of choosing primitive sets (with K. Woods), Journal of Number Theory 125 (2007), 39--49, arxiv:math.NT/0607390.
    
    
13. Restricted Dumont permutations, Dyck paths, and noncrossing partitions (with A. Burnstein and T. Mansour), Discrete Mathematics 306 (2006), 2851-2869, arXiv:math/0610234.
    
    
14. Combinatòria i biologia: funcions d'inferència i alineació de seqüències, Butlletí de la Societat Catalana de Matemàtiques, vol. 21, núm. 1 (2006), 39–52. [Download]
    
    
15. Asymptotic enumeration of permutations avoiding generalized patterns, Advances in Applied Mathematics 36 (2006), 138-155, arXiv:math/0505254.
    
    
16. Inference functions, chapter of the book Algebraic Statistics for Computational Biology, edited by L. Pachter and B. Sturmfels, Cambridge University Press, 2005.
17. 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.
18. Old and young leaves on plane trees (with W.C. Chen and Emeric Deutsch),  European Journal of Combinatorics 27 (2006), 414-427, arXiv:math/0410127.
19. Statistics on Pattern-avoiding Permutations, Ph.D. thesis, MIT, 2004. [Download pdf, ps]
20. Multiple pattern-avoidance with respect to fixed points and excedances, Electronic Journal of Combinatorics 11 (2004), #R51, arXiv:math/0311211.
21. Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials (with T. Mansour), Discrete Mathematics 305 (2005), 170-18, arXiv:math/0610237.
22. A simple and unusual bijection for Dyck paths and its consequences (with E. Deutsch), Annals of Combinatorics 7 (2003), 281-297, arXiv:math/0306125.
23. Bijections for refined restricted permutations (with I. Pak), Journal of Combinatorial Theory - Series A 105 (2004), 207-219, arXiv:math/0212328.
24. Fixed points and excedances in restricted permutations, Proceedings of FPSAC 2003, arxiv:math.CO/0212221.
25. Consecutive patterns in permutations (with M. Noy), Advances in Applied Mathematics 30 (2003), 110-125. [Download]

Some slides of talks I have given

• AMS Fall Eastern Meeting, Special Session on Algebraic Combinatorics, Oct 2009, Descent sets of cyclic permutations. [Slides]
• SODA 2009, January 2009, Sorting by placement and shift. [Slides]
• 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 2-triangulations and pairs of non-crossing Dyck paths. [Slides]
• International Conference on Permutation Patterns, PP'06, Reykjavik, Iceland, June 2006, Generating trees for permutations avoiding generalized patterns. [Slides]
• Institut Mittag-Leffler 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 pattern-avoiding permutations. [Slides]
• International Conference on Permutation Patterns, PP'04, Nanaimo, Canada, July 2004, Simultaneous pattern-avoidance with respect to fixed points and excedances. [Slides]
• Thesis defense, MIT, April 2004, Statistics on Pattern-avoiding Permutations. [Slides]
• UC Berkeley Combinatorics Seminar, February 2004, Refined enumeration of pattern-avoiding permutations. [Slides]
• MIT Combinatorics Seminar, November 2003. Pattern-avoiding 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]

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Some links

- Discrete Mathematics Day conference at Dartmouth, October 2007.
- Old pictures of my friends in Dartmouth, friends in Berkeley, friends in Boston, friends from back home.
- Old pictures of my family (older, not as old).
- Pictures from the FPSAC'03 conference in Vadstena, Sweden.
- My dad's Homepage.
- Iberia: asociación de españoles en Boston.
- Iberia: asociación de españoles en Berkeley.