Sergi Elizalde

http://www.math.dartmouth.edu/~sergi/foto_website1.jpg

Phone:

(603) 646-8191

Dept. Fax:

(603) 646-1312

Office:

332 Kemeny Hall

Office Hours:

M 1:40-3:30
F  11:10-12:20

Email:

 

US Mail:

Department of Mathematics
6188 Kemeny Hall
Dartmouth College
Hanover, NH 03755-3551

 

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

My research interests are mostly in enumerative and algebraic combinatorics. My work so far involves permutations, patterns, bijections, triangulations, lattice paths, generating functions, algorithms, number theory, and applications of combinatorics to computational biology and dynamical systems.

Current teaching

·       Math 13. Multivariable Calculus

·       Math 128. Current Problems in Combinatorics

Ph.D. students

·       Kassie Archer

·       Jonathan Bloom

Here you can download my CV and publication list (not necessarily up to date). After finishing my Ph.D. at MIT with Richard Stanley in 2004, I have been a Postdoctoral Fellow at MSRI, and a John Wesley Young instructor at Dartmouth.

Here is a link to the Dartmouth Combinatorics Seminar webpage.
I co-organized the conference Permutation Patterns 2010. The proceedings will be published in a special issue of Pure Mathematics and Applications.

List of publications and preprints

  1. The most and the least avoided consecutive patterns, preprint, arXiv:1203.1636.

  2. Clusters, generating functions and asymptotics for consecutive patterns in permutations, preprint. [Download]

  3. An involution on lattice paths between two boundaries, preprint. [Download]

  4. A generating tree approach to k-nonnesting partitions and permutations (with M. Mishna, S. Burrill and L. Yen), preprint, arXiv:1108.5615.

  5. Permutations and β-shifts, J. Combin. Theory Ser. A 118 (2011), 2474-2497, arXiv:1008.4167.

  6. Descent sets of cyclic permutations, Adv. in Appl. Math. 47 (2011), 688-709. [Download]

  7. Restricted simsun permutations (with E. Deutsch), Ann. Comb., to appear, arXiv:0912.1361.

  8. On basic forbidden patterns of functions (with Y. Liu), Discrete Appl. Math 159 (2011), 1207-1216, arXiv:0909.2277.

  9. Cycle-up-down permutations (with E. Deutsch), Australas. J. Combin. 50 (2011), 187-199, arXiv:0909.5199.

  10. The X-class and almost-increasing permutations, Ann. Comb. 15 (2011), 51-68, arXiv:0710.5168.

  11. Improved bounds on the number of numerical semigroups of a given genus, J. Pure Appl. Algebra 214 (2010), 1862-1873, arXiv:0905.0489.

  12. The largest and the smallest fixed points of permutations (with E. Deutsch), European J. Combin. 31 (2010), 1404-1409, arXiv:0904.2792.

  13. The number of permutations realized by a shift, SIAM J. Discrete Math. 23 (2009), 765-786. arXiv:0909.2274.

  14. Sorting by Placement and Shift (with P. Winkler), Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2009, arXiv:0809.2957.

  15. Forbidden patterns and shift systems (with J.M. Amigó and M.B. Kennel), J. Combin. Theory Ser. A 115 (2008), 485-504, arXiv:0707.4628.

  16. Generating trees for permutations avoiding generalized patterns, Ann. Comb. 11 (2007), 435-458, arXiv:0707.4633.

  17. A bijection between 2-triangulations and pairs of non-crossing Dyck paths, J. Combin. Theory Ser. A 114/8 (2007), 1481-1503, arxiv:math.CO/0610235.

  18. Bounds on the number of inference functions of a graphical model (with K. Woods), Statist. Sinica 17 (2007), 1395-1415, arxiv:math.CO/0610233.

  19. The probability of choosing primitive sets (with K. Woods), J. Number Theory 125 (2007), 39-49, arxiv:math.NT/0607390.

  20. Restricted Dumont permutations, Dyck paths, and noncrossing partitions (with A. Burstein and T. Mansour), Discrete Math. 306 (2006), 2851-2869, arXiv:math/0610234.

  21. Combinatòria i biologia: funcions d'inferència i alineació de seqüències, Butl. Soc. Catalana Mat. 21 (2006), n. 1, 39–52. [Download]

  22. Asymptotic enumeration of permutations avoiding generalized patterns, Adv. in Appl. Math. 36 (2006), 138-155, arXiv:math/0505254.

  23. Inference functions, chapter of the book Algebraic Statistics for Computational Biology, edited by L. Pachter and B. Sturmfels, Cambridge University Press, 2005.
  24. 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.
  25. Old and young leaves on plane trees (with W.C. Chen and Emeric Deutsch),  European J. Combin. 27 (2006), 414-427, arXiv:math/0410127.
  26. Statistics on Pattern-avoiding Permutations, Ph.D. thesis, MIT, 2004. [Download pdf, ps]
  27. Multiple pattern-avoidance with respect to fixed points and excedances, Electron. J. Combin. 11 (2004), #R51, arXiv:math/0311211.
  28.  Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials (with T. Mansour), Discrete Math. 305 (2005), 170-18, arXiv:math/0610237.
  29. A simple and unusual bijection for Dyck paths and its consequences (with E. Deutsch), Ann. Comb. 7 (2003), 281-297, arXiv:math/0306125.
  30. Bijections for refined restricted permutations (with I. Pak), J. Combin. Theory Ser. A 105 (2004), 207-219, arXiv:math/0212328.
  31. Fixed points and excedances in restricted permutations, Proceedings of FPSAC 2003, arxiv:math.CO/0212221.
  32. Consecutive patterns in permutations (with M. Noy), Adv. in Appl. Math. 30 (2003), 110-125. [Download]


Some slides of talks I have given

Past teaching

Links

- Permutation Patterns 2010 at Dartmouth, August 9-13, 2010.
- Discrete Mathematics Day at Dartmouth, October 2007.
- My dad's homepage.
- Iberia: asociación de españoles en Boston.
- Iberia: asociación de españoles en Berkeley.