2025/07/21 by Qipin Chen, Chen, Qipin, Shane Chern +3
Materials Science · Mathematics · #05B45 #82B20 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Primary 15A15 #Quasicrystal Structures and Properties #Secondary 05A15 #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.2507.15665
openalex publication_date 2025/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Koutschan, Krattenthaler and Schlosser recently considered a family of binomial determinants. In this work, we give combinatorial interpretations of two subclasses of these determinants in terms of domino tilings and nonintersecting lattice paths, thereby partially answering a question of theirs. Furthermore, the determinant evaluations established by Koutschan, Krattenthaler and Schlosser produce many product formulas for our weighted enumerations of domino tilings and nonintersecting lattice paths. However, there are still two enumerations left corresponding to conjectural formulas made by the three. We hereby prove the two conjectures using the principle of holonomic Ansatz plus the approach of modular reduction for creative telescoping, and hence fill the gap.