The research of Catherine Yan has been supported by the National Science Foundation, the National Security Agency, Simon's Foundation, and a Qatar National Research Fund.
Recent Publications
68. Multivariate Difference Goncarov Polynomials, joint with Ayo Adeniran, Lauren Snider. 2020. Submitted. (17 pages).
67. On Increasing and Invariant Parking Functionss, joint with Ayo Adeniran. Australas. J. Combin. Vol. 79(1), 2021. pp 167--182.
66. Parking Functions on Directed Graphs and some Directed Trees, joint with W. King. Electro. J. Combin. Volume 27, Issue 2(2020), P2.48. (16 pages)
65. Goncarov Polynomials in Partition Lattices and Exponential Families . Joint with A. Adeniran. (23 pages). Adv. Appl. Math. published online April 2020, at here
64. Vector parking functions with periodic boundaries and rational parking functions , joint with Yue Cai. Journal of Combinatorial Theory A, volume 173, July 2020. 105239. 30 pages.
63. Prime Parking Functions on Rooted Trees , joint with W. King. J. Combina. Theory A. Vol. 168, 2019, page 1-25.
62. Counting with Borel's Triangle , Joint with Y. Cai, Discrete Mathematics, Vol 342(2), 2019, 529--539.
61. Parking Functions on Oriented Trees , joint with W. King. Extended Abstract. 30th International Conference on Formal Power Series and Algebraic Combinatorics, 2018.Seminaire Lotharingien de Combinatoire. 80B (2018), Art. 47, 12 pp.
60. Generalized Goncarov Polynomials , Joint with Rudolph Lorentz and Salvatore Tringali. Connections in Discrete Mathematics: A Celebration of the Work of Ron Graham, S. Butler et al. (Eds.) Cambridge University Press 2018. page 56-85.
59. Parking Distributions on Trees , Joint with Ron Graham and Steve Butler. European Journal of Combinatorics, 65 (2017), 168-185.
58. Multivariate Delta Goncarov and Abel Polynomials , Joint with Rudolph Lorentz and Salvatore Tringali. Journal of Mathematical Analysis and Applications 446 (2017), pp 663-680. Available online 7 September 2016.
57. Moments of Matching Statistics , Joint with Niraj Khare and Rudolph Lorentz. Journal of Combinatorics, Vol. 8, No. 1(2017), pp. 1-27.
56. Bivariate Affine Goncarov Polynomials , Joint with Rudolph Lorentz. Discrete Mathematics, Discrete Mathematics 339 (2016), pp. 2371-2383.
55. Parking Functions, Chapter 13 in Handbook of Enumerative Combinatorics, edited by Miklos Bona. Chapman and Hall/CRC, 2015. ISBN 9781482220858.
54. Derangements on a Ferrers board , joint with W. Linz. Discrete Mathematics, Algorithms and Applications, 2015. Vol. 07, No. 03. 1550036. DOI: 10.1142/S1793830915500366
53. Avoiding monotone chains in fillings of layer polyominoes , joint with M. Phillipson. Annals of Combinatorics, 20(4), 883--897, 2016. Available online August 3, 2016.
52. Maximal increasing sequences in fillings of almost-moon polyominoes , joint with Svetlana Poznanovic, Advances in Applied Mathematics, 66(2015), 1--21.
51. Bivariate Goncarov polynomials and integer sequences , joint with Niraj Khare and Rudolph Lorentz. Science China Mathematics Volume 57 Issue 8(2014), 1561-1578. published on line May 16, 2014. DOI: 10.1007/s11425-014-4827-x.
50. Chains of length 2 in fillings of layer polyominoes , joint with M. Phillipson and J. Yeh. Electronic Journal of Combinatorics, Volume 20, Issue 3 (2013), Paper 51.
49. Positive and Negative Chains in Charged Moon Polyominoes , joint with A. Wang. Advances in Applied Mathematics 51 (2013) 467--482. DOI 10.1016/j.aam.2013.06.001.
48. On the enumeration of non-crossing pairings of well-balanced binary strings , joint with P. Schumacher. Annals of Combiatorics, Vol 17, Issue 2 (2013), 379--391. Published online in January 10, 2013.
47. Descents of permutations in a Ferrers board , joint with C. Song. Electronic Journal of Combinatorics, Volume 19 (2012), issue 1, Paper 7. (16 pages)
46. High-energy String Sacttering Amplitudes and Signless Stirling Number Identity , joint with J-C. Lee and Y. Yang. Symmetry, Integrabiity and Geometry: Methods and Applications, 8 (2012), 045, 9 pages.
45. Mixed statistics on 01-fillings of moon polyominoes , joint with W.Y.C Chen, A. Y. Z. Wang, and A. F. Y. Zhao. SIAM Journal on Discrete Mathematics, Vol. 24 (2010) issue 4, 1272--1290. An Extended abstract is published at Discrete Mathematics and Theoretical Computer Science, DMTCS proc. AN, 2010, 481--492.
44. Major index for moon polyominoes , joint with W.Y.C. Chen, S. Poznanovik, and A.L.B. Yang. Journal of Combinatorial Theory, Ser. A. Vol. 117 (2010), no.8, 1058--1081.
43. Crossings and nestings of two edges in set partitions , joint with S. Poznanovik. SIAM Journal of Discrete Mathematics. vol.23, no.2. (2009) 787-804. Talk slides
42. Lattice and Schroder paths with periodic boundaries , joint with J. Kung, A. de Mier, and X. Sun. Journal of Statistical Planning and Inference, vol. 139, issue 6, (2009) 2014--2027.
41. A Major Index for Matchings and Set Partitions, joint with W.Y.C. Chen, I. Gessel and A.L. Yang, Jounal of Combinatorial Theory Series A, vol 115, (2008) 1069--1076. A longer version with a bijective proof is here .
40. How to play the one-lie Renyi-Ulam game , joint with R. Ellis and V. Ponomarenko, accepted by Discrete Mathematics. Vol 208(2008), no 23, 5805--5808.
39. Multiparking Functions, Graph Search, and Tutte Polynomial. joint with D. Kostic, Advances in Applied Mathematics, Vol. 40 (2008), 73-97.
38. Linked Partitions and Linked Cycles, joint with W.Y.C. Chen and S.Y. Wu, European Journal of Combinatorics, vol 29, issue 6 (2008), 1408--1426.
37. Two-Boundary Lattice Paths and Parking Functions. , J. Kung, X. Sun and C.H. Yan. Advances in Applied Mathematics, vol. 39 (2007), 515--524.
36. Random Geometric Graph Diameter in the Unit Ball. R. Ellis, J. Martin and C.H. Yan. Algorithmica, volume 47, no. 4, (2007), 421--438.
35. Crossing and Nestings of Matchings and Partitions. W.Y.C. Chen, E.Y.P. Deng, R.R.X.Du, R.P.Stanley and C.H. Yan. Trans. Amer. Math. Soc. volume 359, no. 4, (2007) 1555--1575.
34. On Random Points in the Unit Disk , pdf file , R. Ellis, X. Jia and C. H. Yan, Random Algorithm and Structures.Volume 29, Issue 1 (2006), 14--25. Published online, December 12, 2005.
33. Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings , R. Graham, J.C. Lagarias, C.L. Mallows, A.R. Wilks, and C. H. Yan, Discrete and Computational Geometry, 35:1--36(2006). The original publication will be available at Springer's website. An author-created copy is available at archive math.MG/0010302. (37 pages).
32. Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions , R. Graham, J.C. Lagarias, C.L. Mallows, A.R. Wilks, and C. H. Yan, Discrete and Computational Geometry. 35:37--72(2006). The original publication will be available at Springer's website. An author-created copy is available at archive math.MG/0010302. (37 pages)
31. Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group , R. Graham, J.C. Lagarias, C.L. Mallows, A.R. Wilks, and C. H. Yan, Discrete and Computational Geometry 34:547--585(2005). The original publication will be available at Springer's website. An author-created copy is available at archive math.MG/0010298. (42 pages)
30. Random Geometric Graph Diameter in the Unit Disk with $\ell_p$ Metric, (Extended Abstract) R. Ellis, J. Martin and C. H. Yan. in Lecture Notes in Computer Science, Vol. 3383, pp167. Springer-Verlag, 2005.
29. The Renyi-Ulam Pathological Liar Game with a Fixed Number of Lies pdf file, R. Ellis, V. Ponomarenko and C. H. Yan. Journal of Combinatorial Theory, Series A, 112(2005) 328--336.
28. Ulam's Pathological Liar Game with One Half-lie. R. Ellis and C. H. Yan. International Journal of Mathematics and Mathematical Sciences, 2004:29(2004), 1523--1532.
27. The Halflie Problem (pdf file, 21 pages), J. Spencer, and C. H. Yan, Journal of Combinatorial Theory, Series A, vol 103(2003), 69--89.
26. Exact Formula for Moments of Sums of Classical Parking Functions . J. Kung and C. H. Yan. Advances in Applied Mathematics, vol 31(2003), 215--241.
25. Goncarov Polynomials and Parking Functions, J. Kung and C. H. Yan, Journal of Combinatorial Theory, Series A, vol. 102, no.1 (2003), 16--37.
24. Branching processes with Negative Offspring Distributions, . I. Dumitriu, J. Spencer, and C. H. Yan, Annals of Combinatorics, vol 7(2003), 35--47.
23. Expected Sums of Moments General Parking Functions, J. Kung and C. H. Yan, Annals of Combinatorics, vol. 7(2003), 481--493.
22. Generating Functions for Moments of the Quasi-Nilpotent DT-Operator , K. Dykema and C. H. Yan, Advances in Applied Mathematics, vol. 30, no.3 (2003), 545--561.
21. Apollonian Circle Packings: Number Theory, (pdf file, 54 pages). R. Graham, J.C. Lagarias, C.L. Mallows, A.R. Wilks, and C. H. Yan, Journal of Number Theory, vol.100, no.1 (2003), 1--45.
20. Six Problems of Gian-Carlo Rota in Lattice Theory and Universal Algebra, (pdf file, 14 pages). J. Kung and C. H. Yan, Algebra Universalis, vol. 49(2003), 113--127.
19. Hirzebruch $\chi_y$ Genera of the Hilbert Schemes of Surfaces by Localization Formula , K. Liu, C. H. Yan and J. Zhou, Sci. China Ser. A. (2002), no. 4, 420--431.
18. Generalized Parking Functions, Tree Inversions and Multicolored Graphs , C. H. Yan. Advances in Applied Mathematics, Vol. 27, 641--670, 2001.
17. Geometric Identities in Lattice Theory. M. Mainetti and C. H. Yan, Journal of Combinatorial Theory A, vol. 91, No. 1/2 (2000), 411--450.
16. Arguesian Identities in the Congruence Variety of Abelian Groups, C. H. Yan, Advances in Mathematics, vol. 150, (2000), 36--79.
15. On the Enumeration of Generalized Parking Functions , C. H. Yan, Congressus Numerantium, Proceedings of the 31st Southeastern International Conference on Combinatorics, Graph Theory, and Computing, (Boca Raton, 2000). Congressus Numerantium, 147 (2000), 201--209.
14. On Discrepancy of Strongly Unimodular Matricses , H. Peng and C. H. Yan, Discrete Mathematics, vol. 219 (2000), 223-333.
13. Arguesian Identities in Linear Lattices, M. Mainetti and C. H. Yan, Advances in Mathematics, vol. 144, (1999), 50--93.
12. Theory of Commuting Boolean Sigma-Algebras, C. H. Yan, Advances in Mathematics, vol. 144, (1999), 94--116.
11. On the Limit of a Recurrence Relation, R. Graham and C. H. Yan, Journal of Difference Equations and Aplications, Vol. 5 (1999), 71--95.
10. Balancing Game with a Buffer, H. Peng and C. H. Yan, Advances in Applied Mathematics, 21(2), (1998) 193--204.
9. The Theory of Commuting Subalgebras of a Complete Heyting Algebra, J. Crants and C. H. Yan, Advances in Mathematics, vol. 139(2), (1998) 260--292.
8. Decomposition of Lebesgue Spaces , C. H. Yan, Advances in Mathematics, vol. 135(2), (1998) 330--350, (1998).
7. Graphical Operations on Projective Spaces, M. Mainetti and C. H. Yan, Annals of Combinatorics, vol. 2, No. 3 (1998) 245—291.
6. Commuting Quasi-order Relations , C. H. Yan, Discrete Mathematics, 183(1--3) (1998) 285--292.
5. Distributive Laws for Commuting Equivalence Relations, C. H. Yan, Discrete Mathematics, 181(1--3) (1998) 295--298.
4. Quasifinite Representations of Classical Lie Subalgebras of $W_{1+\infty}$ , V. G. Kac, W. Wang and C. H. Yan, Advances in Mathematics, vol. 139(1), (1998) 59--140.
3. Quasifinite Highest Weight Modules over the Lie Algebra of Matrix Differential Operators on the Circle , C. Boyallian, V. G. Kac, J. I. Liberati and C. H. Yan, Journal of Mathematical Physics, vol. 39(5), (1998) 2910--2928.
2. Generalized Tree Inversions and $k$-Parking Functions , C. H. Yan, Journal of combinatorial theory A, vol. 79(2), (1997) 268--280.
1 Avoiding Like Runs in Cyclic Strings , C. Fox and C. H. Yan, SPUR report of M.I.T., August 1997.
Other Preprints
An Enumeration Problem and Branching Processes, (pdf file, 20 pages). J. Spencer and C. H. Yan. Preprint, 2001.
Goncarov-Type polynomials and Applications in Combinatorics , joint with J. Kung and X. Sun, preprint, 2006.