Papers
- Perfect matchings of cellular graphs,
J. Algebraic Combin. 5 (1996), 87-103.
- A remark on sets having the Steinhaus property,
Combinatorica 16 (3) (1996), 321-324.
- Enumeration of perfect matchings in graphs with
reflective symmetry, J. Combin. Theory Ser. A 77 (1997), 67-97.
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Enumeration of rhombus tilings of a hexagon which contain a fixed rhombus on its symmetry axis (21 p)
(with C. Krattenthaler and M. Fulmek), arXiv preprint, 1997.
- A complementation theorem for perfect matchings of graphs having a cellular
completion, J. Combin. Theory Ser. A 81 (1998), 34-68.
- An improved upper bound for the three dimensional dimer problem,
Duke Math. J. 94 (1998),
1-11.
- No-feedback card guessing for dovetail shuffles,
Ann. Appl. Prob. 8 (1998), 1251-1269.
- Enumeration of lozenge tilings of punctured hexagons,
J. Combin. Theory Ser. A 83 (1998),
268-272.
- The number of centered lozenge tilings of a symmetric hexagon
(with C. Krattenthaler),
J. Combin. Theory Ser. A 86 (1999), 103-126.
- The equivalence between enumerating cyclically symmetric,
self-complementary and totally symmetric, self-complementary plane
partitions,
J. Combin. Theory Ser. A 86 (1999), 382-389.
- Higher dimensional Aztec diamonds and the (2^d+2)-vertex model,
J. Algebraic Combin. 9 (1999), 281-293.
- Plane partitions II: 5 1/2 symmetry classes
(with C. Krattenthaler), Advanced Studies in Pure Mathematics 28 (2000), 83-103.
- Enumeration of lozenge tilings of hexagons
with a central triangular hole (with T. Eisenkolbl, C.
Krattenthaler and D. Zare), J. Combin. Theory Ser. A 95 (2001), 251-334.
- A non-automatic (!) application of Gosper's
algorithm evaluates a determinant from tiling enumeration (with C.
Krattenthaler), Rocky Mountain J. Math., 32 (2002), 589--605.
- Enumeration of lozenge tilings of hexagons with
cut off corners (with C. Krattenthaler), J. Combin. Theory Ser. A,
100 (2002), 201-231 .
- Perfect matchings and perfect powers,
J. Algebraic Combin., 17 (2003), 335-375.
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The number of spanning trees of plane graphs with reflective symmetry
(with W. Yan and F. Zhang), J. Combin. Theory Ser. A, 112 (2005), no. 1, 105-116.
- Rotational invariance of quadromer correlations on the hexagonal lattice,
Adv. in Math., 191 (2005), 46
- Plane partitions I: A generalization of
MacMahon's formula, Memoirs of Amer. Math. Soc., 178 (2005),
no. 839, 107-144.
(arXiv preprint math.CO/9808017).
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A random tiling model for two dimensional electrostatics,
Memoirs of Amer. Math. Soc., 178 (2005),
no. 839, 1-106. (arXiv preprint math-ph/0303067).
- A visual proof of a result of Knuth on spanning trees of Aztec diamonds
in the case of odd order,
Discrete Math. 307 (2007), 1957-1960.
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Symmetry classes of spanning trees of Aztec diamonds and perfect matchings of
odd squares with a unit hole,
J. of Algebraic Combin., 27 (2008), 493-538.
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Dimer packings with gaps and electrostatics, Proc. Natl. Acad. Sci. USA,
105 (2008), 2766-2772.
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The scaling limit of the correlation of holes on the triangular lattice with periodic boundary
conditions, Memoirs of Amer. Math. Soc. 199 (2009), no. 935, 1-100.
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A factorization theorem for classical group characters, with applications to plane partitions and rhombus tilings (with C. Krattenthaler), Advances in Combinatorial Mathematics: Proceedings of the Waterloo Workshop in Computer Algebra 2008, I. Kotsireas, E. Zima (eds.), Springer-Verlag, 2009, 39-60.
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The emergence of the electrostatic field as a Feynman sum in random tilings with holes, Trans. Amer. Math. Soc. 362 (2010), 4921-4954.
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A Casimir force in dimer systems, in ``Casimir Force, Casimir operators, and the Riemann Hypothesis,'' Mathematics for Innovation in Industry and Science, Ed. by Gerrit van Dijk and Masato Wakayama, De Gruyter Proceedings in Mathematics, 2010.
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Perfect matchings and applications, COE Lecture Note, 26. Math-for-Industry Lecture Note Series, Kyushu University, Faculty of Mathematics, Fukuoka, 2010, 1-67.
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The interaction of a gap with a free boundary in a two dimensional dimer
system (with C. Krattenthaler), Comm. Math. Phys. 302 (2011), 253-289.
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Enumeration of perfect matchings of Fisher graphs of cubic graphs
(with Y. Liu and C. Yang), Kyushu Journal of Mathematics 66 (2012), 291-302.
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A triangular gap of side 2 in a sea of dimers in a 60 degree angle
(with I. Fischer), J. Phys. A: Math. Theor. 45 (2012), 494011.
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A dual of MacMahon's theorem on plane partitions
(with C. Krattenthaler), Proc. Natl. Acad. Sci. USA 110
(2013), 4518-4523.
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Proof of Blum's conjecture on hexagonal dungeons
(with Tri Lai), J. Combin. Theory Ser. A 125 (2014), 273-305.
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The interaction of collinear gaps of arbitrary charge in a two dimensional dimer system
, Comm. Math. Phys. 330 (2014), 1115--1153.
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Lozenge tilings with gaps in a 90 degree wedge domain with mixed
boundary conditions
, Comm. Math. Phys. 334 (2015), 507-532.
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Proof of two conjectures of Ciucu and Krattenthaler on the
enumeration of lozenge tilings of hexagons with cut off corners
(with Ilse Fischer), J. Combin. Theory Ser. A 133 (2015), 228-250.
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A generalization of Kuo condensation
, J. Combin. Theory Ser. A 134 (2015), 221-241.
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A factorization theorem for lozenge tilings of a hexagon with
triangular holes
(with Christian Krattenthaler), Trans. Amer. Math. Soc.
369 (2017), 3655-3672.
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Macroscopically separated gaps in dimer coverings of Aztec
rectangles
, Comm. Math. Phys. 344 (2016), 223-274.
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Lozenge tilings of hexagons with arbitrary dents,
(with Ilse Fischer), Adv. Appl. Math. 73 (2016), 1-22.
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Four factorization formulas for plane partitions,
Proc. of Amer. Math. Soc. 144 (2016), 1841-1856.
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A short conceptual proof of Narayana's path-counting formula,
Electron. J. Comb. 23 (2016), Paper P4.11.
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The other dual of MacMahon's theorem on plane partitions,
Adv. in Math. 306 (2017), 427-450.
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Gaps in dimer systems on doubly periodic planar bipartite graphs,
Proc. of Amer. Math. Soc. 145 (2017), 4931-4944.
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Symmetries of shamrocks, Part I,
J. Combin. Theory Ser A 155 (2018), 376-397.
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Symmetries of Shamrocks II: Axial Shamrocks,
Electron. J. Comb. 25 (2018), Paper P2.36.
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Lozenge tilings of doubly-intruded hexagons,
(with Tri Lai), J. Combin. Theory Ser A, 167 (2019), 294-339.
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Centrally symmetric tilings of fern-cored hexagons, arxiv preprint, 2019.
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Correlation of a macroscopic dent in a wedge with mixed boundary
conditions, Trans. Amer. Math. Soc. 373 (2020), 2173-2190.
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Symmetries of shamrocks IV: The self-complementary case,
Proc. Amer. Math. Soc. 149 (2021), 935-951.
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Tilings of hexagons with a removed triad of bowties (with Tri Lai
and Ranjan Rohatgi), J. Combin. Theory Ser. A 178 (2021), Paper No. 105359, 39 pp.
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The effect of microscopic gap displacement on the correlation of gaps in dimer systems,
J. Stat. Phys. 186 (2022), Paper No. 18, 35 pp.
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Cruciform regions and a conjecture of Di Francesco,
Proc. Amer. Math. Soc. 150 (2022), 4655-4670.
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Lozenge tilings of hexagons with removed core and satellites (with
Ilse Fischer), Ann. Inst. Henri Poincaré D 10 (2023), no. 3, 407-501.
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Two counterparts of the TFK formula for cylinder graphs,
J. Combin. Theory Ser. A 196 (2023), Paper No. 105722, 31 pp.
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Boundary dents, the arctic circle and the arctic ellipse (with Christian Krattenthaler),
arxiv preprint, 2023.