Tiling Enumeration

Results:

• A bijective look at gapfree partitions: between local and global
  Shane Chern, Shishuo Fu, Dazhao Tang
  Ramanujan J (2025) Vol. 67, Nr. 34.
  doi: 10.1007/s11139-025-01078-7 (associated to Project 6)
• Multiple Rogers-Ramanujan type identities for torus links
  Shane Chern
  arXiv:2411.07198 (associated to Project 6)
• A generalization of conjugation of integer partitions
  Seamus Albion, Theresia Eisenkölbl, Ilse Fischer, Moritz Grangl, Hans Höngesberg, Christian Krattenthaler, Martin Rubey
  Electronic J. Combin. (2025),  Vol. 32, Nr. 2.
  DOI:10.37236/13489 (associated to Project 4 and 6)
• Arithmetic properties of the Taylor coefficients of differentially algebraic power series
  Christian Krattenthaler, Tanguy Rivoal
  arXiv:2502.09259 (associated to Project 6)
• A positivity conjecture for a quotient of q-binomial coefficients
  Mona Gatzweiler, Christian Krattenthaler
  Ramanujan J. (2026), Vol. 69, No. 1
  DOI: 10.1007/s11139-025-01285-2 (associated to Project 6)
• Refined enumeration of two-rowed set-valued standard tableaux via two-coloured Motzkin paths
  Christian Krattenthaler
  arXiv:2501.09208 (associated to Project 6)
• An Orthogonal View of Gaußian Polynomials
  Christian Krattenthaler, Brandt Kronholm, Paul Marsh
  arXiv:2510.14124 (associated to Project 6)
• Bounded Littlewood identities with fixed number of odd rows or odd columns
  JiSun Huh, Jang Soo Kim, Christian Krattenthaler, Soichi Okada
  arXiv:2510.11054 (associated to Project 6)
• Schur log-concavity and the quantum Pascal triangle
  Álvaro Gutiérrez, Christian Krattenthaler
  arXiv:2509.22648 (associated to Project 6)
• A probabilistic proof of Euler's pentagonal number theorem
  Shane Chern
  Sém. Lothar. Combin. 92 (2025), Art. B92c, 12 pp (associated to Project 6)
• Convolutive sequences, I: Through the lens of integer partition functions
  Shane Chern, Dennis Eichhorn, Shishuo Fu, James A. Sellers
  Exp. Math, in press.
  DOI: 10.1080/10586458.2025.2604777 (associated to Project 6)
• Domino tilings, nonintersecting lattice paths and subclasses of Koutschan–Krattenthaler–Schlosser determinants
  Qipin Chen, Shane Chern, Atsuro Yoshida
  J. Combin. Theory Ser. A (2026), Vol. 221, Paper No. 106159, 37pp.
  DOI: 10.1016/j.jcta.2026.106159 (associated to Project 4 and 6)
• Signed counting of partition matrices
  Shane Chern, Shishuo Fu
  arXiv:2508.21318 (associated to Project 6)
• Asymptotics for the enumeration of commuting matrices over finite fields
  Kathrin Bringmann, Shane Chern, Johann Franke, Bernhard Heim
  SIGMA Symmetry Integrability Geom. Methods Appl. (2026), Vol. 22, Paper No. 016, 8 pp. 
  DOI: 10.3842/SIGMA.2026.016 (associated to Project 6)
• Proof of the Andrews-El Bachraoui positivity conjecture
  Shane Chern, Chun Wang
  arXiv:2601.19845 (associated to Project 6)
• Signed counting of partition matrices
  Shane Chern, Shishuo Fu
  J. Combin. Theory Ser. A (2026), Vol. 223, Paper No. 106213, 32 pp.
  DOI: 10.1016/j.jcta.2026.106213 (associated to Project 6)
• On conjectural fermionic formulas for the Macdonald index in Argyres–Douglas theories
  Shane Chern, Chanh Tran, Tanay Wakhare
  arXiv:2605.02251 (associated to Project 6)