Research
My research interests are mostly in enumerative and algebraic combinatorics. Here are a few keywords from my papers: permutations, patterns, lattice paths, bijections, triangulations, generating functions. I have also done some work on algorithms, number theory, and applications of combinatorics to computational biology and dynamical systems.

Recent preprints

Journal publications

  1. On rotated Schur-positive sets (with Y. Roichman), J. Combin. Theory Ser. A 152 (2017), 121-137. arXiv:1609.07335.

  2. Character formulas and descents for the hyperoctahedral group (with R. Adin, C. Athanasiadis and Y. Roichman), Adv. in Appl. Math. 87 (2017), 128-169. arXiv:1504.01283.

  3. The structure of the consecutive pattern poset (with P. McNamara), Int. Math. Res. Not. IMRN 2017, doi:10.1093/imrn/rnw293. arXiv:1508.05963.

  4. Statistics on bargraphs viewed as cornerless Motzkin paths (with E. Deutsch), Discrete Appl. Math. 221 (2017), 54-66.. arXiv:1609.00088.

  5. Two descent statistics over 321-avoiding centrosymmetric involutions (with M. Barnabei, F. Bonetti and M. Silimbani), Electron. J. Combin. 23 (2016), #P1.35. arXiv:1508.07515.

  6. Schur-positive sets of permutations via products of grid classes (with Y. Roichman), J. Algebraic Combin. 45 (2017), 363-405. arXiv:1509.00045.

  7. Symmetries of statistics on lattice paths between two boundaries (with M. Rubey), Adv. Math. 287 (2016), 347-388. arXiv:1305.2206.

  8. Dynamics of tumor heterogeneity derived from clonal karyotypic evolution (with A. Laughney, S. Bakhoum and G. Genovese), Cell Rep. 12 (2015), 809-820.

  9. Bijections for pairs of non-crossing lattice paths and walks in the plane, European J. Combin. 49 (2015), 25-41. arXiv:1406.1709.

  10. Signed arc permutations (with Y. Roichman), J. Comb. 6 (2015), 205-234. arXiv:1402.0211.

  11. A generating tree approach to k-nonnesting partitions and permutations (with M. Mishna, S. Burrill and L. Yen), Ann. Comb. 20 (2016), 453-485. arXiv:1108.5615.

  12. Descent sets on 321-avoiding involutions and hook decompositions of partitions (with M. Barnabei, F. Bonetti , and M. Silimbani), J. Combin. Theory Ser. A 128 (2014), 132-148. arXiv:1401.3011.

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

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

  15. Inversion polynomials for 321-avoiding permutations (with S.-E. Cheng, A. Kasraoui and B. Sagan), Discrete Math. 313 (2013), 2552-2565. arXiv:1112.6014 (addendum: arXiv:1305.3845).

  16. Total occurrence statistics on restricted permutations (with A. Burstein), Pure Math. Appl. (PU.M.A.) 24 (2013), 103-123. arXiv:1305.3177.

  17. The most and the least avoided consecutive patterns, Proc. Lond. Math. Soc. 106 (2013), 957-979. arXiv:1203.1636.

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

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

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

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

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

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

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

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

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

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

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

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

  30. 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.

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

  32. 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.

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

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

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

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

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

  38. Old and young leaves on plane trees (with W.C. Chen and Emeric Deutsch), European J. Combin. 27 (2006), 414-427. arXiv:math/0410127.

  39. Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials (with T. Mansour), Discrete Math. 305 (2005), 170-189. arXiv:math/0610237.

  40. Multiple pattern-avoidance with respect to fixed points and excedances, Electron. J. Combin. 11 (2004), #R51. arXiv:math/0311211.

  41. Bijections for refined restricted permutations (with I. Pak), J. Combin. Theory Ser. A 105 (2004), 207-219. arXiv:math/0212328.

  42. A simple and unusual bijection for Dyck paths and its consequences (with E. Deutsch), Ann. Comb. 7 (2003), 281-297. arXiv:math/0306125.

  43. Consecutive patterns in permutations (with M. Noy), Adv. in Appl. Math. 30 (2003), 110-125. [Download]

Book Chapters

  1. A survey of consecutive patterns in permutations, chapter of the book Recent Trends in Combinatorics (IMA Volume in Mathematics and its Applications) 601-618, Springer, 2016. arXiv:1504.07265.

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

  3. 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. A necessary condition for c-Wilf equivalence (with T. Dwyer), Sem. Lothar. Combin. 78B (2017), Article #69, 12 pp.

  2. Patterns of negative shifts and signed shifts (with K. Archer and K. Moore), Sem. Lothar. Combin. 78B (2017), Article #49, 12 pp.

  3. Schur-positivity via products of grid classes (with Y. Roichman), Proceedings of FPSAC 2016, Discrete Math. Theor. Comput. Sci. proc. BC (2016), 443--454.

  4. On intervals of the consecutive pattern poset (with P. McNamara), Proceedings of FPSAC 2016, Discrete Math. Theor. Comput. Sci. proc. BC (2016), 431--442.

  5. The frequency of pattern occurrence in random walks (with M. Martinez), Proceedings of FPSAC 2015, Discrete Math. Theor. Comput. Sci. proc. FPSAC'15 (2015), 217-228.

  6. Periodic patterns of signed shifts (with K. Archer), Proceedings of FPSAC 2013, Discrete Math. Theor. Comput. Sci. proc. AS (2013), 873-884.

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

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

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

  10. 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.

  11. 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.

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

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

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

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

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

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

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

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

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

  21. Forbidden subwords in permutations (with M. Noy), Proceedings of FPSAC 2001.

Unpublished material

Some slides of talks I have given