SAT for Mathematics

Papers and resources on using satisfiability solvers in mathematics.

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126 papers


  • A counterexample to the Etzion-Silberstein conjecture

    Jitendra Prajapati

  • A SAT Attack on Tarski's High School Algebra Problem

    Bernardo Subercaseaux, Benjamin Przybocki

  • Voting Method Synthesis on an Infinite Domain: A Possibility Theorem for Positive Involvement

    Wesley H. Holliday

  • One-Weight Colorings, the Symmetric Class, and Lower Bounds for Hales--Jewett Numbers

    Younes Mouhib

  • A Lean-Certified Proof of K8(4,2)=23K_8(4, 2) = 23

    Andreas Florath

  • There are matroid toric ideals without quadratic Gröbner bases

    Jesús A. De Loera, Luis Ferroni, Santiago Morales, Jörg Rambau

  • Witness-split + window-cardinality refinement for r3(N)r_3(N): Architecture, empirical results, and a structural hard pocket

    Mehmet Ergezer

  • Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discovery

    Benjamin Przybocki, John Mackey, Marijn J. H. Heule, Bernardo Subercaseaux

  • A Counterexample to EFX n3n \ge 3 Agents, mn+5m \ge n + 5 Items, Submodular Valuations via SAT-Solving

    Hannaneh Akrami, Alexander Mayorov, Kurt Mehlhorn, Shreyas Srinivas, Christoph Weidenbach

  • A SAT-based Filtering Framework for Exact Coverings of K33 by Cliques of Order 3, 4 or 5

    Petr Kovař, Yifan Zhang

  • Constraint Satisfaction Programming for the No-three-in-line Problem

    Thomas Prellberg

  • Two-colorings of finite grids: variations on a theorem of Tibor Gallai

    Bogdan Dumitru, Mihai Prunescu

  • North-East Lattice Paths Avoiding kk Collinear Points via Satisfiability

    Aaron Barnoff, Curtis Bright

  • OOPS: Optimized One-Planarity Solver via SAT

    Sergey Pupyrev

  • From the Finite to the Infinite: Sharper Asymptotic Bounds on Norin's Conjecture via SAT

    Markus Kirchweger, Tomáš Peitl, Bernardo Subercaseaux, Stefan Szeider

  • Depth-13 Sorting Networks for 28 Channels

    Chengu Wang

  • A note on irreducibility for topical maps

    Brian Lins

  • New bounds for some small multicolor Ramsey numbers

    William J. Wesley

  • Queen Domination by SAT Solving

    Taha Rostami, Curtis Bright

  • The 3-Decomposition Conjecture: A SAT-Based Approach with Specialized Propagators

    Tianwei Zhang, Stefan Szeider

  • Constructing Optimal Kobon Triangle Arrangements via Table Encoding, SAT Solving, and Heuristic Straightening

    Pavlo Savchuk

  • Constructing strong starters of orders 3p3p: triplication with SAT solver

    Oleg Ogandzhanyants, Sergey Sadov, Margo Kondratieva

  • Unfolding Boxes with Local Constraints

    Long Qian, Eric Wang, Bernardo Subercaseaux, Marijn J. H. Heule

  • Automated Symmetric Constructions in Discrete Geometry

    Bernardo Subercaseaux, Ethan Mackey, Long Qian, Marijn J. H. Heule

  • Investigating Simple Drawings of K_n Using SAT

    Helena Bergold, Manfred Scheucher

  • Counterexample to Winkler's Conjecture on Venn Diagrams

    Sofia Brenner, Linda Kleist, Torsten Mütze, Christian Rieck, Francesco Verciani

  • Verified Certificates via SAT and Computer Algebra Systems for the Ramsey R(3, 8) and R(3, 9) Problems

    Zhengyu Li, Conor Duggan, Curtis Bright, Vijay Ganesh

  • Smart Cubing for Graph Search: A Comparative Study

    Markus Kirchweger, Hai Xia, Tomáš Peitl, Stefan Szeider

  • Incremental SAT-Based Enumeration of Solutions to the Yang-Baxter Equation

    Daimy Van Caudenberg, Bart Bogaerts, Leandro Vendramin

  • Myrvold's Results on Orthogonal Triples of 10 x 10 Latin Squares: A SAT Investigation

    Curtis Bright, Amadou Keita, Brett Stevens

    • arXiv · 2025
  • Optimal Partitions of the Flat Torus into Parts of Smaller Diameter

    Dmitry Protasov, Alexander Tolmachev, Vsevolod Voronov

    • Discrete Optimization · 2025
  • The Borsuk Problem for Subsets of the Vertices of the 10-Dimensional Boolean Cube

    Igor Batmanov, Vsevolod Voronov

    • arXiv · 2025
  • Lower Bounds for Book Ramsey Numbers

    William J. Wesley

  • Proving Norine's Conjecture Holds for n=7n = 7 via SAT Solvers

    Keith Frankston, Danny Scheinerman

  • The chromatic number of 4-dimensional lattices

    Frank Vallentin, Stephen Weißbach, Marc Christian Zimmermann

  • Detecting Isohedral Polyforms with a SAT Solver

    Craig S. Kaplan

  • Using Finite Automata to Compute the Base-b Representation of the Golden Ratio and Other Quadratic Irrationals

    Aaron Barnoff, Curtis Bright, Jeffrey Shallit

  • Happy Ending: An Empty Hexagon in Every Set of 30 Points

    Marijn J. H. Heule, Manfred Scheucher

  • Finding Hardness Reductions Automatically Using SAT Solvers

    Helena Bergold, Manfred Scheucher, Felix Schröder

  • A SAT Solver + Computer Algebra Attack on the Minimum Kochen-Specker Problem

    Zhengyu Li, Curtis Bright, Vijay Ganesh

  • Computing Small Rainbow Cycle Numbers with SAT Modulo Symmetries

    Markus Kirchweger, Stefan Szeider

    • CP · 2024
  • PackIt! Gamified Rectangle Packing

    Thomas Garrison, Marijn J. H. Heule, Bernardo Subercaseaux

  • SAT-Based Search for Minwise Independent Families

    Enrico Iurlano, Günther R. Raidl

    • arXiv · 2024
  • Automated Mathematical Discovery and Verification: Minimizing Pentagons in the Plane

    Bernardo Subercaseaux, John Mackey, Marijn J. H. Heule, Ruben Martins

  • Structure and Computability of Preimages in the Game of Life

    Ville Salo, Ilkka Törmä

  • The Pancake Graph of Order 10 Is 4-Colorable

    Renzo Roel Perez Tan, Aldrich Ellis Catapang Asuncion, Brian Godwin Sy Lim, Mate Soos, Kazushi Ikeda

  • On the Deque and Rique Numbers of Complete and Complete Bipartite Graphs

    Michael A. Bekos, Michael Kaufmann, Maria Eleni Pavlidi, Xenia Rieger

  • Using SAT to Study Plane Hamiltonian Substructures in Simple Drawings

    Helena Bergold, Stefan Felsner, Meghana M. Reddy, Manfred Scheucher

  • A SAT Solver's Opinion on the Erdős-Faber-Lovász Conjecture

    Markus Kirchweger, Tomáš Peitl, Stefan Szeider

  • Combinatorial Designs Meet Hypercliques: Higher Lower Bounds for Klee’s Measure Problem and Related Problems in Dimensions d ≥ 4

    Egor Gorbachev, Marvin Künnemann

  • Investigating the~Existence of~Holey Latin Squares via~Satisfiability Testing

    Minghao Liu, Rui Han, Fuqi Jia, Pei Huang, Feifei Ma, Hantao Zhang, Jian Zhang

  • On a Pair of Orthogonal Golf Designs

    Hong Lu, Jianpeng Chen, Haitao Cao

    • Discrete Mathematics · 2023
  • Searching for Smallest Universal Graphs and Tournaments with SAT

    Tianwei Zhang, Stefan Szeider

    • CP · 2023
  • Toward Optimal Radio Colorings of Hypercubes via SAT-solving

    Bernardo Subercaseaux, Marijn J. H. Heule

    • LPAR · 2023
  • Using a SAT Solver to Find Interesting Sets of Nonstandard Dice

    Michael Purcell

  • Impossibility Theorems Involving Weakenings of Expansion Consistency and Resoluteness in Voting

    Wesley H. Holliday, Chase Norman, Eric Pacuit, Saam Zahedian

  • Improved Lower Bounds for Multicolour Ramsey Numbers using SAT-Solvers

    Fred Rowley

  • A SAT Attack on Rota's Basis Conjecture

    Markus Kirchweger, Manfred Scheucher, Stefan Szeider

    • SAT · 2022
  • On Using SAT Solvers for Graph Computations

    Bruno Courcelle, Irène A. Durand

    • preprint · 2022
  • The Packing Chromatic Number of the Infinite Square Grid Is at Least 14

    Bernardo Subercaseaux, Marijn J. H. Heule

    • SAT · 2022
  • When Satisfiability Solving Meets Symbolic Computation

    Curtis Bright, Ilias S. Kotsireas, Vijay Ganesh

  • New lower bounds for Schur and weak Schur numbers

    Romain Ageron, Paul Casteras, Thibaut Pellerin, Yann Portella, Arpad Rimmel, Joanna Tomasik

  • A Counterexample to the Unit Conjecture for Group Rings

    Giles Gardam

  • Avoiding Monochromatic Rectangles Using Shift Patterns

    Zhenjun Liu, Leroy Chew, Marijn J. H. Heule

  • A SAT-based Resolution of Lam's Problem

    Curtis Bright, Kevin K. H. Cheung, Brett Stevens, Ilias S. Kotsireas, Vijay Ganesh

  • Search for developments of a box having multiple ways of folding by SAT solver

    Riona Tadaki, Kazuyuki Amano

  • A nonexistence certificate for projective planes of order ten with weight 15 codewords

    Curtis Bright, Kevin K. H. Cheung, Brett Stevens, Dominique Roy, Ilias S. Kotsireas, Vijay Ganesh

  • Coloring Unit-Distance Strips Using SAT

    Peter Oostema, Ruben Martins, Marijn J. H. Heule

  • Effective Problem Solving Using SAT Solvers

    Curtis Bright, Jürgen Gerhard, Ilias S. Kotsireas, Vijay Ganesh

  • Fast Formal Proof of the Erdős--Szekeres Conjecture for Convex Polygons with at Most 6 Points

    Filip Marić

    • Journal of Automated Reasoning · 2019
  • SAT solvers and computer algebra systems: a powerful combination for mathematics

    Curtis Bright, Ilias S. Kotsireas, Vijay Ganesh

  • The SAT+CAS method for combinatorial search with applications to best matrices

    Curtis Bright, Dragomir Ž. Đoković, Ilias S. Kotsireas, Vijay Ganesh

  • Computing Small Unit-Distance Graphs with Chromatic Number 5

    Marijn J. H. Heule

  • The Chromatic Number of the Plane Is at Least 5

    Aubrey D. N. J. de Grey

  • A SAT+CAS Method for Enumerating Williamson Matrices of Even Order

    Curtis Bright, Ilias S. Kotsireas, Vijay Ganesh

  • Improving Circuit Size Upper Bounds Using SAT-solvers

    Alexander S. Kulikov

  • Investigating the Existence of Large Sets of Idempotent Quasigroups via Satisfiability Testing

    Pei Huang, Feifei Ma, Cunjing Ge, Jian Zhang, Hantao Zhang

    • Automated {{Reasoning}} · 2018
  • A SAT Attack on the Erdős-Szekeres Conjecture

    Martin Balko, Pavel Valtr

  • Combining SAT Solvers with Computer Algebra Systems to Verify Combinatorial Conjectures

    Edward Zulkoski, Curtis Bright, Albert Heinle, Ilias S. Kotsireas, Krzysztof Czarnecki, Vijay Ganesh

  • Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer

    Marijn J. H. Heule, Oliver Kullmann, Victor W. Marek

  • MathCheck2: A SAT+CAS Verifier for Combinatorial Conjectures

    Curtis Bright, Vijay Ganesh, Albert Heinle, Ilias S. Kotsireas, Saeed Nejati, Krzysztof Czarnecki

  • Non Existence of Some Mixed Moore Graphs of Diameter 2 Using SAT

    Nacho López, Josep M. Miret, Cèsar Fernández

  • MathCheck: A Math Assistant via a Combination of Computer Algebra

    Edward Zulkoski, Vijay Ganesh, Krzysztof Czarnecki

  • The Book Embedding Problem from a SAT-Solving Perspective

    Michael A. Bekos, Michael Kaufmann, Christian Zielke

  • Breaking Symmetries in Graph Representation

    Michael Codish, Alice Miller, Patrick Prosser, Peter J. Stuckey

  • Solution of the Last Open Four-Colored Rectangle-Free Grid: An Extremely Complex Multiple-Valued Problem

    Bernd Steinbach, Christian Posthoff

  • Symmetry in Gardens of Eden

    Christiaan Hartman, Marijn J. H. Heule, Kees Kwekkeboom, Alain Noels

  • A New Lower Bound for the Ramsey Number R(4, 8)

    Hiroshi Fujita

  • Upward Planarity Testing via SAT

    Markus Chimani, Robert Zeranski

  • Solving Rubik's Cube Using SAT Solvers

    Jingchao Chen

  • A SAT-based Method for Solving the Two-dimensional Strip Packing Problem

    Takehide Soh, Katsumi Inoue, Naoyuki Tamura, Mutsunori Banbara, Hidetomo Nabeshima

    • Fundamenta Informaticae · 2010
  • Two New Van Der Waerden Numbers: W(2; 3, 17) and w(2; 3, 18)

    Tanbir Ahmed

    • INTEGERS · 2010
  • Satisfiability and Computing van Der Waerden Numbers

    Michael R. Dransfield, Victor W. Marek, Mirosław Truszczyński