Sergi Elizalde

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

Phone:

(603) 646-8191

Dept. Fax:

(603) 646-1312

Office:

332 Kemeny Hall

Office Hours:

Tu 9-10:30,
Fr 11:05-12:30

Email:

 

US Mail:

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

 

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 co-organizing 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 co-organized the conference Permutation Patterns 2010. The proceedings have been published in a special issue of Pure Mathematics and Applications.


Recent Preprints

  1. Symmetries of statistics on lattice paths between two boundaries (with M. Rubey), preprint, arXiv:1305.2206.

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

Journal Publications

  1. Cyclic permutations realized by signed shifts (with K. Archer), J. Comb. 5 (2014), 1—30. arXiv:1304.7790.

  2. Inversion polynomials for 321-avoiding permutations (with S.-E. Cheng, A. Kasraoui and B. Sagan), Discrete Math. 313 (2013), 2552-2565. arXiv:1112.6014.

  3. Arc permutations (with Y. Roichman), J. Algebraic Combin. 39 (2014), 301—334. arXiv:1210.6056.

  4. Total occurrence statistics on restricted permutations (with A. Burstein), Pure Math. Appl. (PU.M.A.), to appear. arXiv:1305.3177.

  5. Pattern avoidance in matchings and partitions (with J. Bloom), Electron. J. Combin. 20 (2013), #P5. arXiv:1211.3442.

  6. The most and the least avoided consecutive patterns, Proc. Lond. Math. Soc. 106 (2013), 957—979, doi: 10.1112/plms/pds063. arXiv:1203.1636.

  7. Clusters, generating functions and asymptotics for consecutive patterns in permutations (with M. Noy), Adv. in Appl. Math. 49 (2012), 351–374. arXiv:1210.6061.

  8. Fixed points and excedances in restricted permutations, Electron. J. Combin. 18 (2012), #P29.

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

  10. Descent sets of cyclic permutations, Adv. in Appl. Math. 47 (2011), 688-709. arXiv:0906.2795.

  11. Restricted simsun permutations (with E. Deutsch), Ann. Comb. 16 (2012), 253–269. arXiv:0912.1361.

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

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

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

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

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

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

  18. 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.

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

  20. 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.

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

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

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

  24. Combinatňria i biologia: funcions d'inferčncia i alineació de seqüčncies, Butl. Soc. Catalana Mat. 21 (2006), n. 1, 39–52. [Download]

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

  26. Old and young leaves on plane trees (with W.C. Chen and Emeric Deutsch), European J. Combin. 27 (2006), 414-427, arXiv:math/0410127.
  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. Consecutive patterns in permutations (with M. Noy), Adv. in Appl. Math. 30 (2003), 110-125. [Download]

Book Chapters

  1. Inference functions, chapter of the book Algebraic Statistics for Computational Biology, edited by L. Pachter and B. Sturmfels, Cambridge University Press, 2005.
  2. 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

  1. Periodic patterns of signed shifts (with K. Archer), Discrete Math. Theor. Comput. Sci. proc. AS (2013), 873-884. [Download extended abstract].

  2. Patterns in matchings and rook placements (with J. Bloom), Discrete Math. Theor. Comput. Sci. proc. AS (2013), 909-920.

  3. Bijections for lattice paths between two boundaries (with M. Rubey), Proceedings of FPSAC 2012, Discrete Math. Theor. Comput. Sci. proc. AR (2012), 827-838.

  4. Arc Permutations (extended abstract) (with Y. Roichman), Proceedings of FPSAC 2012, Discrete Math. Theor. Comput. Sci. proc. AR (2012), 259-270.

  5. Consecutive patterns in permutations: clusters and generating functions (with M. Noy), Proceedings of FPSAC 2012, Discrete Math. Theor. Comput. Sci. proc. AR (2012), 247-258.

  6. Generating trees for partitions and permutations with no k-nestings (with M. Mishna, S. Burrill and L. Yen), Proceedings of FPSAC 2012, Discrete Math. Theor. Comput. Sci. proc. AR (2012), 409-420.

  7. Allowed patterns of beta-shifts, Proceedings of FPSAC 2011, Discrete Math. Theor. Comput. Sci. proc. AO (2011), 293-304.

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

  9. Permutations realized by shifts, Proceedings of FPSAC 2009, Discrete Math. Theor. Comput. Sci. proc. AK (2009), 361-372.

  10. Pattern avoidance in dynamical systems (with J.M. Amigó, M.B. Kennel), Proceedings of FPSAC 2008, Discrete Math. Theor. Comput. Sci. proc. AJ (2008), 71-82.

  11. A bijection between 2-triangulations and pairs of non-crossing Dyck paths, Proceedings of FPSAC 2007.

  12. Bounds on the number of inference functions of a graphical model (with K. Woods), Proceedings of FPSAC 2006.

  13. Old and young leaves on plane and binary trees (with E. Deutsch), Proceedings of FPSAC 2005.

  14. Restricted Motzkin permutations (with T. Mansour), Proceedings of FPSAC 2004.

  15. Fixed points and excedances in restricted permutations, Proceedings of FPSAC 2003, arxiv:math.CO/0212221.

  16. 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 Pattern-avoiding Permutations, Ph.D. thesis, MIT, 2004. [Download pdf, ps]


Some slides of talks I have given


Past teaching


Links

- Richard Stanley's 70th birthday conference, MIT, June 23-27, 2014.
- Permutation Patterns 2010 at Dartmouth, August 9-13, 2010.
- Discrete Mathematics Day at Dartmouth, October 2007.
- Discrete Math Days permanent website.