The research of Catherine Yan has been supported by the National Science Foundation, the National Security Agency, and a Qatar National Research Fund.

**Recent Publications **

**62.
Prime Parking Functions on Rooted Trees , joint with W. King. 2018.
**

**61.
Counting with Borel's Triangle **, Joint with Y. Cai, preprint 2017.

**60.
Parking Distributions on Trees **, Joint with Ron Graham and Steve Butler.
European Journal of Combinatorics, 65 (2017), 168-185.

**59.
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.

**58.
Generalized Goncarov Polynomials **, Joint with Rudolph Lorentz and Salvatore Tringali.
to appear in S. Butler et al. (Eds.), Connections in Discrete Mathematics: A Celebration
of the Work of Ron Graham, Cambridge University Press.

**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.