Sergi Elizalde

	Phone:	(603) 646-8191
	Dept. Fax:	(603) 646-1312
	Office:	332 Kemeny Hall
	Office Hours:	M 1:40-3:30 W 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 118. Combinatorics.

Ph.D. students

· Kassie Archer

· Jonathan Bloom

· Megan Ehresmann

Here you can download my CV and publication list with abstracts. 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 (maintained by R. Orellana). Let us know if you are interested in giving a talk.
I co-organized the conference Permutation Patterns 2010. The proceedings have been published in a special issue of Pure Mathematics and Applications.

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Recent Preprints

1. Symmetries of statistics on lattice paths between two boundaries (with M. Rubey), preprint, arXiv:1305.2206.
   
   
2. Inversion polynomials for 321-avoiding permutations (with S.-E. Cheng, A. Kasraoui and B. Sagan), preprint, arXiv:1112.6014.
   
   
3. Cyclic permutations realized by signed shifts (with K. Archer), preprint, arXiv:1304.7790.
   
   
4. 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. Arc permutations (with Y. Roichman), J. Algebraic Combin., to appear, arXiv:1210.6056.
   
   
2. Total occurrence statistics on restricted permutations (with A. Burstein), Pure Math. Appl. (PU.M.A.), to appear, arXiv:1305.3177.
   
   
3. Pattern avoidance in matchings and partitions (with J. Bloom), Electron. J. Combin. 20 (2013), #P5. arXiv:1211.3442.
   
   
4. The most and the least avoided consecutive patterns, Proc. Lond. Math. Soc., to appear, doi: 10.1112/plms/pds063. arXiv:1203.1636.
   
   
5. Clusters, generating functions and asymptotics for consecutive patterns in permutations (with M. Noy), Adv. in Appl. Math. 49 (2012), 351–374. arXiv:1210.6061.
   
   
6. Fixed points and excedances in restricted permutations, Electron. J. Combin. 18 (2012), #P29.
   
   
7. Permutations and β-shifts, J. Combin. Theory Ser. A 118 (2011), 2474-2497. arXiv:1008.4167.
   
   
8. Descent sets of cyclic permutations, Adv. in Appl. Math. 47 (2011), 688-709. arXiv:0906.2795.
   
   
9. Restricted simsun permutations (with E. Deutsch), Ann. Comb. 16 (2012), 253–269. arXiv:0912.1361.
   
   
10. On basic forbidden patterns of functions (with Y. Liu), Discrete Appl. Math 159 (2011), 1207-1216. arXiv:0909.2277.
    
    
11. Cycle-up-down permutations (with E. Deutsch), Australas. J. Combin. 50 (2011), 187-199. arXiv:0909.5199.
    
    
12. The X-class and almost-increasing permutations, Ann. Comb. 15 (2011), 51-68. arXiv:0710.5168.
    
    
13. Improved bounds on the number of numerical semigroups of a given genus, J. Pure Appl. Algebra 214 (2010), 1862-1873. arXiv:0905.0489.
    
    
14. The largest and the smallest fixed points of permutations (with E. Deutsch), European J. Combin. 31 (2010), 1404-1409. arXiv:0904.2792.
    
    
15. The number of permutations realized by a shift, SIAM J. Discrete Math. 23 (2009), 765-786. arXiv:0909.2274.
    
    
16. 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.
    
    
17. Generating trees for permutations avoiding generalized patterns, Ann. Comb. 11 (2007), 435-458. arXiv:0707.4633.
    
    
18. 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.
    
    
19. Bounds on the number of inference functions of a graphical model (with K. Woods), Statist. Sinica 17 (2007), 1395-1415, arxiv:math.CO/0610233.
    
    
20. The probability of choosing primitive sets (with K. Woods), J. Number Theory 125 (2007), 39-49, arxiv:math.NT/0607390.
    
    
21. Restricted Dumont permutations, Dyck paths, and noncrossing partitions (with A. Burstein and T. Mansour), Discrete Math. 306 (2006), 2851-2869, arXiv:math/0610234.
    
    
22. Combinatòria i biologia: funcions d'inferència i alineació de seqüències, Butl. Soc. Catalana Mat. 21 (2006), n. 1, 39–52. [Download]
    
    
23. Asymptotic enumeration of permutations avoiding generalized patterns, Adv. in Appl. Math. 36 (2006), 138-155, arXiv:math/0505254.
    
    
24. Old and young leaves on plane trees (with W.C. Chen and Emeric Deutsch), European J. Combin. 27 (2006), 414-427, arXiv:math/0410127.
25. Multiple pattern-avoidance with respect to fixed points and excedances, Electron. J. Combin. 11 (2004), #R51, arXiv:math/0311211.
26. Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials (with T. Mansour), Discrete Math. 305 (2005), 170-18, arXiv:math/0610237.
27. A simple and unusual bijection for Dyck paths and its consequences (with E. Deutsch), Ann. Comb. 7 (2003), 281-297, arXiv:math/0306125.
28. Bijections for refined restricted permutations (with I. Pak), J. Combin. Theory Ser. A 105 (2004), 207-219, arXiv:math/0212328.
29. 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), Proceedings of FPSAC 2013. [Download extended abstract].
   
   
2. Patterns in matchings and rook placements (with J. Bloom), Proceedings of FPSAC 2013.
   
   
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

• Bijections for lattice paths between two boundaries [SIAM DM'12 Slides].
• Consecutive patterns in permutations: clusters, generating functions, and asymptotics [Slides Feb 2012]
• Allowed patterns of β-shifts [FPSAC 2011 Slides]. Permutations and β-shifts [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 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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Past teaching

• Winter 2013: Math 17. An Introduction to Math Beyond Calculus.
• Spring 2012: Math 13. Multivariable Calculus, Math 128. Current Problems in Combinatorics.
• Fall 2011: Math 68. Algebraic Combinatorics.
• Winter 2011: Math 28. Introduction to Combinatorics; Math 118. Combinatorics.
• Spring 2010: Math 38. Graph Theory.
• Winter 2010: Math 28. Introduction to Combinatorics; Math 81. Abstract Algebra.
• Winter 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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Links

- Permutation Patterns 2010 at Dartmouth, August 9-13, 2010.
- Discrete Mathematics Day at Dartmouth, October 2007.