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MSC Classification Numbers (651)
- 00-XX General (11)
  - 00-01 Instructional exposition (textbooks, tutorial papers, etc.) (1)
  - 00Axx General and miscellaneous specific topics (6)
    - 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.) (3)
    - 00A15 Bibliographies (1)
    - 00A69 General applied mathematics (1)
    - 00A71 Theory of mathematical modeling (1)
    - 00A79 Physics (use more specific entries from Sections 70 through 86 when possible) (1)
  - 00Bxx Conference proceedings and collections of papers (5)
    - 00B15 Collections of articles of miscellaneous specific content (1)
    - 00B25 Proceedings of conferences of miscellaneous specific interest (2)
    - 00B30 Festschriften (2)
- 01-XX History and biography (4)
  - 01-06 Proceedings, conferences, collections, etc. (1)
  - 01-08 Computational methods (1)
  - 01Axx History of mathematics and mathematicians (2)
    - 01A70 Biographies, obituaries, personalia, bibliographies (2)
- 03-XX Mathematical logic and foundations (22)
  - 03Bxx General logic (22)
    - 03B05 Classical propositional logic (17)
    - 03B70 Logic in computer science (2)
    - 03B99 None of the above, but in this section (2)
- 05-XX Combinatorics (247)
  - 05-01 Instructional exposition (textbooks, tutorial papers, etc.) (1)
  - 05-02 Research exposition (monographs, survey articles) (5)
  - 05Axx Classical combinatorial problems (6)
    - 05A15 Exact enumeration problems, generating functions (5)
    - 05A18 Partitions of sets (1)
  - 05Bxx Designs and configurations (63)
    - 05B15 Orthogonal arrays, Latin squares, Room squares (1)
    - 05B20 Matrices (incidence, Hadamard, etc.) (1)
    - 05B35 Matroids, geometric lattices (54)
    - 05B40 Packing and covering (10)
    - 05B50 Polyominoes (1)
  - 05Cxx Graph theory (190)
    - 05C05 Trees (17)
    - 05C07 Vertex degrees (1)
    - 05C10 Planar graphs; geometric and topological aspects of graph theory (37)
    - 05C12 Distance in graphs (9)
    - 05C15 Coloring of graphs and hypergraphs (11)
    - 05C17 Perfect graphs (2)
    - 05C20 Directed graphs (digraphs), tournaments (14)
    - 05C21 Flows in graphs (2)
    - 05C22 Signed and weighted graphs (2)
    - 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) (5)
    - 05C30 Enumeration in graph theory (3)
    - 05C35 Extremal problems (7)
    - 05C38 Paths and cycles (21)
    - 05C40 Connectivity (10)
    - 05C45 Eulerian and Hamiltonian graphs (10)
    - 05C50 Graphs and matrices (9)
    - 05C62 Graph representations (geometric and intersection representations, etc.) (8)
    - 05C65 Hypergraphs (4)
    - 05C69 Dominating sets, independent sets, cliques (18)
    - 05C70 Factorization, matching, covering and packing (22)
    - 05C75 Structural characterization of types of graphs (14)
    - 05C78 Graph labelling (graceful graphs, bandwidth, etc.) (1)
    - 05C83 Graph minors (3)
    - 05C85 Graph algorithms (58)
    - 05C90 Applications (7)
    - 05C99 None of the above, but in this section (16)
  - 05Dxx Extremal combinatorics (1)
    - 05D05 Extremal set theory (1)
- 06-XX Order, lattices, ordered algebraic structures (25)
  - 06-04 Explicit machine computation and programs (1)
  - 06-06 Proceedings, conferences, collections, etc. (1)
  - 06Axx Ordered sets (11)
    - 06A05 Total order (1)
    - 06A06 Partial order, general (6)
    - 06A07 Combinatorics of partially ordered sets (4)
    - 06A11 Algebraic aspects of posets (1)
  - 06Bxx Lattices (5)
    - 06B20 Varieties of lattices (1)
    - 06B30 Topological lattices, order topologies (3)
  - 06Cxx Modular lattices, complemented lattices (5)
    - 06C10 Semimodular lattices, geometric lattices (5)
  - 06Dxx Distributive lattices (1)
    - 06D50 Lattices and duality (1)
- 11-XX Number theory (9)
  - 11Hxx Geometry of numbers (4)
    - 11H31 Lattice packing and covering (4)
  - 11Jxx Diophantine approximation, transcendental number theory (1)
    - 11J85 Algebraic independence; Gelfond's method (1)
  - 11Txx Finite fields and commutative rings (number-theoretic aspects) (1)
    - 11T71 Algebraic coding theory; cryptography (1)
  - 11Yxx Computational number theory (3)
    - 11Y05 Factorization (3)
- 12-XX Field theory and polynomials (3)
  - 12Exx General field theory (3)
    - 12E15 Skew fields, division rings (3)
- 15-XX Linear and multilinear algebra; matrix theory (2)
  - 15Axx Basic linear algebra (2)
    - 15A18 Eigenvalues, singular values, and eigenvectors (2)
- 18-XX Category theory; abstract homological algebra (4)
  - 18Bxx Special categories (4)
    - 18B99 None of the above, but in this section (4)
- 20-XX Group theory and generalizations (11)
  - 20Bxx Permutation groups (9)
    - 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures (7)
    - 20B40 Computational methods (2)
  - 20Cxx Representation theory of groups (1)
    - 20C20 Modular representations and characters (1)
  - 20Exx Structure and classification of infinite or finite groups (1)
    - 20E28 Maximal subgroups (1)
  - 20Gxx Linear algebraic groups (classical groups) (1)
    - 20G40 Linear algebraic groups over finite fields (1)
  - 20Mxx Semigroups (1)
    - 20M99 None of the above, but in this section (1)
  - 20Nxx Other generalizations of groups (1)
    - 20N15 n-ary systems (n >= 3) (1)
- 28-XX Measure and integration (1)
  - 28Axx Classical measure theory (1)
    - 28A75 Length, area, volume, other geometric measure theory (1)
- 35-XX Partial differential equations (1)
  - 35Qxx Equations of mathematical physics and other areas of application (1)
    - 35Q30 Stokes and Navier-Stokes equations (1)
- 37-XX Dynamical systems and ergodic theory (8)
  - 37Axx Ergodic theory (3)
    - 37A35 Entropy and other invariants, isomorphism, classification (1)
    - 37A50 Relations with probability theory and stochastic processes (1)
    - 37A99 None of the above, but in this section (1)
  - 37Mxx Approximation methods and numerical treatment of dynamical systems (5)
    - 37M10 Time series analysis (5)
- 41-XX Approximations and expansions (1)
  - 41A30 Approximation by other special function classes (1)
- 49-XX Calculus of variations and optimal control; optimization (5)
  - 49Jxx Existence theories (2)
    - 49J20 Optimal control problems involving partial differential equations (1)
    - 49J35 Minimax problems (2)
  - 49Kxx Necessary conditions and sufficient conditions for optimality (1)
    - 49K40 Sensitivity, stability, well-posedness (1)
  - 49Mxx Methods of successive approximations (2)
    - 49M20 Methods of relaxation type (1)
    - 49M30 Other methods, not based on necessary conditions (penalty function, etc.) (1)
    - 49M37 Methods of nonlinear programming type (1)
  - 49Nxx Miscellaneous topics (1)
    - 49N15 Duality theory (1)
- 51-XX Geometry (16)
  - 51Axx Linear incidence geometry (2)
    - 51A20 Configuration theorems (1)
    - 51A45 Incidence structures imbeddable into projective geometries (1)
  - 51Dxx Geometric closure systems (4)
    - 51D20 Combinatorial geometries (4)
  - 51Exx Finite geometry and special incidence structures (2)
    - 51E20 Combinatorial structures in finite projective spaces (1)
    - 51E25 Other finite nonlinear geometries (1)
  - 51Hxx Topological geometry (3)
    - 51H20 Topological geometries on manifolds (3)
  - 51Mxx Real and complex geometry (6)
    - 51M04 Elementary problems in Euclidean geometries (1)
    - 51M05 Euclidean geometries (general) and generalizations (1)
    - 51M16 Inequalities and extremum problems (4)
  - 51Nxx Analytic and descriptive geometry (1)
    - 51N20 Euclidean analytic geometry (1)
- 52-XX Convex and discrete geometry (33)
  - 52Axx General convexity (1)
    - 52A10 Convex sets in 2 dimensions (including convex curves) (1)
  - 52Bxx Polytopes and polyhedra (27)
    - 52B05 Combinatorial properties (number of faces, shortest paths, etc.) (5)
    - 52B10 Three-dimensional polytopes (1)
    - 52B12 Special polytopes (linear programming, centrally symmetric, etc.) (11)
    - 52B20 Lattice polytopes (including relations with commutative algebra and algebraic geometry) (2)
    - 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (11)
    - 52B55 Computational aspects related to convexity (1)
  - 52Cxx Discrete geometry (8)
    - 52C17 Packing and covering in n dimensions (5)
    - 52C35 Arrangements of points, flats, hyperplanes (2)
    - 52C40 Oriented matroids (1)
- 53-XX Differential geometry (1)
  - 53Axx Classical differential geometry (1)
    - 53A07 Higher-dimensional and -codimensional surfaces in Euclidean n-space (1)
  - 53Cxx Global differential geometry (1)
    - 53C40 Global submanifolds (1)
- 57-XX Manifolds and cell complexes (1)
  - 57Nxx Topological manifolds (1)
    - 57N50 S^ (1)
- 58-XX Global analysis, analysis on manifolds (1)
  - 58Exx Variational problems in infinite-dimensional spaces (1)
    - 58E35 Variational inequalities (global problems) (1)
- 60-XX Probability theory and stochastic processes (35)
  - 60C05 Combinatorial probability (5)
  - 60D05 Geometric probability, stochastic geometry, random sets (1)
  - 60Exx Distribution theory (5)
    - 60E15 Inequalities; stochastic orderings (5)
  - 60Fxx Limit theorems (1)
    - 60F05 Central limit and other weak theorems (1)
  - 60Gxx Stochastic processes (2)
    - 60G07 General theory of processes (1)
    - 60G42 Martingales with discrete parameter (1)
  - 60Jxx Markov processes (8)
    - 60J20 Applications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.) (7)
    - 60J99 None of the above, but in this section (1)
  - 60Kxx Special processes (19)
    - 60K30 Applications (congestion, allocation, storage, traffic, etc.) (19)
    - 60K35 Interacting random processes; statistical mechanics type models; percolation theory (1)
- 62-XX Statistics (12)
  - 62-07 Data analysis (4)
  - 62Hxx Multivariate analysis (2)
    - 62H30 Classification and discrimination; cluster analysis (2)
  - 62Mxx Inference from stochastic processes (1)
    - 62M05 Markov processes - estimation (1)
  - 62Nxx Survival analysis and censored data (1)
    - 62N99 None of the above, but in this section (1)
  - 62Pxx Applications (6)
    - 62P10 Applications to biology and medical sciences (6)
- 65-XX Numerical analysis (36)
  - 65-04 Explicit machine computation and programs (not the theory of computation or programming) (2)
  - 65Bxx Acceleration of convergence (1)
    - 65B99 None of the above, but in this section (1)
  - 65Cxx Probabilistic methods, simulation and stochastic differential equations (7)
    - 65C05 Monte Carlo methods (3)
    - 65C20 Models, numerical methods (3)
    - 65C99 None of the above, but in this section (1)
  - 65Fxx Numerical linear algebra (2)
    - 65F50 Sparse matrices (2)
  - 65Kxx Mathematical programming, optimization and variational techniques (17)
    - 65K05 Mathematical programming (12)
    - 65K10 Optimization and variational techniques (4)
    - 65K99 None of the above, but in this section (1)
  - 65Nxx Partial differential equations, boundary value problems (1)
    - 65N15 Error bounds (1)
    - 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (1)
    - 65N55 Multigrid methods; domain decomposition (1)
  - 65Yxx Computer aspects of numerical algorithms (7)
    - 65Y05 Parallel computation (6)
    - 65Y10 Algorithms for specific classes of architectures (1)
  - 65Z05 Applications to physics (1)
- 68-XX Computer science (266)
  - 68-01 Instructional exposition (textbooks, tutorial papers, etc.) (2)
  - 68-02 Research exposition (monographs, survey articles) (1)
  - 68-04 Explicit machine computation and programs (not the theory of computation or programming) (7)
  - 68-06 Proceedings, conferences, collections, etc. (2)
  - 68Mxx Computer system organization (12)
    - 68M07 Mathematical problems of computer architecture (2)
    - 68M10 Network design and communication (2)
    - 68M14 Distributed systems (1)
    - 68M20 Performance evaluation; queueing; scheduling (9)
  - 68Nxx Software (14)
    - 68N17 Logic programming (2)
    - 68N20 Compilers and interpreters (7)
    - 68N25 Operating systems (2)
  - 68Pxx Theory of data (7)
    - 68P05 Data structures (2)
    - 68P10 Searching and sorting (2)
    - 68P15 Database theory (1)
    - 68P25 Data encryption (1)
    - 68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (1)
  - 68Qxx Theory of computing (75)
    - 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.) (4)
    - 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (7)
    - 68Q25 Analysis of algorithms and problem complexity (65)
  - 68Rxx Discrete mathematics in relation to computer science (93)
    - 68R01 General (1)
    - 68R05 Combinatorics (28)
    - 68R10 Graph theory (54)
    - 68R15 Combinatorics on words (3)
    - 68R99 None of the above, but in this section (12)
  - 68Txx Artificial intelligence (13)
    - 68T05 Learning and adaptive systems (1)
    - 68T10 Pattern recognition, speech recognition (4)
    - 68T15 Theorem proving (deduction, resolution, etc.) (3)
    - 68T20 Problem solving (heuristics, search strategies, etc.) (2)
    - 68T50 Natural language processing (1)
  - 68Uxx Computing methodologies and applications (54)
    - 68U05 Computer graphics; computational geometry (18)
    - 68U10 Image processing (2)
    - 68U20 Simulation (31)
    - 68U99 None of the above, but in this section (1)
  - 68Wxx Algorithms (66)
    - 68W01 General (17)
    - 68W10 Parallel algorithms (15)
    - 68W25 Approximation algorithms (12)
    - 68W35 VLSI algorithms (11)
    - 68W40 Analysis of algorithms (10)
    - 68W99 None of the above, but in this section (3)
- 70-XX Mechanics of particles and systems (1)
  - 70Fxx Dynamics of a system of particles, including celestial mechanics (1)
    - 70F10 n-body problems (1)
- 76-XX Fluid mechanics (1)
  - 76Fxx Turbulence (1)
    - 76F05 Isotropic turbulence; homogeneous turbulence (1)
- 80-XX Classical thermodynamics, heat transfer (1)
  - 80Axx Thermodynamics and heat transfer (1)
    - 80A99 None of the above, but in this section (1)
- 81-XX Quantum theory (1)
  - 81Qxx General mathematical topics and methods in quantum theory (1)
    - 81Q99 None of the above, but in this section (1)
- 82-XX Statistical mechanics, structure of matter (33)
  - 82-08 Computational methods (1)
  - 82Bxx Equilibrium statistical mechanics (4)
    - 82B41 Random walks, random surfaces, lattice animals, etc. (3)
    - 82B99 None of the above, but in this section (1)
  - 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) (18)
    - 82C22 Interacting particle systems (3)
    - 82C32 Neural nets (1)
    - 82C70 Transport processes (14)
  - 82Dxx Applications to specific types of physical systems (13)
    - 82D30 Random media, disordered materials (including liquid crystals and spin glasses) (12)
- 90-XX Operations research, mathematical programming (277)
  - 90-01 Instructional exposition (textbooks, tutorial papers, etc.) (3)
  - 90-02 Research exposition (monographs, survey articles) (6)
  - 90-06 Proceedings, conferences, collections, etc. (3)
  - 90-08 Computational methods (10)
  - 90Bxx Operations research and management science (95)
    - 90B05 Inventory, storage, reservoirs (9)
    - 90B06 Transportation, logistics (28)
    - 90B10 Network models, deterministic (15)
    - 90B15 Network models, stochastic (6)
    - 90B18 Communication networks (3)
    - 90B20 Traffic problems (21)
    - 90B22 Queues and service (1)
    - 90B25 Reliability, availability, maintenance, inspection (2)
    - 90B30 Production models (4)
    - 90B35 Scheduling theory, deterministic (21)
    - 90B40 Search theory (3)
    - 90B50 Management decision making, including multiple objectives (2)
    - 90B70 Theory of organizations, manpower planning (1)
    - 90B85 Continuous location (2)
    - 90B90 Case-oriented studies (1)
  - 90Cxx Mathematical programming (224)
    - 90C05 Linear programming (22)
    - 90C06 Large-scale problems (3)
    - 90C08 Special problems of linear programming (transportation, multi-index, etc.) (6)
    - 90C09 Boolean programming (10)
    - 90C10 Integer programming (46)
    - 90C11 Mixed integer programming (17)
    - 90C20 Quadratic programming (11)
    - 90C22 Semidefinite programming (4)
    - 90C25 Convex programming (4)
    - 90C26 Nonconvex programming (1)
    - 90C27 Combinatorial optimization (130)
    - 90C30 Nonlinear programming (22)
    - 90C31 Sensitivity, stability, parametric optimization (1)
    - 90C32 Fractional programming (1)
    - 90C34 Semi-infinite programming (2)
    - 90C35 Programming involving graphs or networks (39)
    - 90C39 Dynamic programming (13)
    - 90C46 Optimality conditions, duality (2)
    - 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut (21)
    - 90C59 Approximation methods and heuristics (10)
    - 90C60 Abstract computational complexity for mathematical programming problems (4)
    - 90C90 Applications of mathematical programming (25)
- 91-XX Game theory, economic, social and behavioral sciences (40)
  - 91Axx Game theory (22)
    - 91A05 2-person games (2)
    - 91A10 Noncooperative games (1)
    - 91A12 Cooperative games (11)
    - 91A20 Multistage and repeated games (1)
    - 91A25 Dynamic games (1)
    - 91A40 Game-theoretic models (1)
    - 91A43 Games involving graphs (5)
    - 91A46 Combinatorial games (3)
    - 91A65 Hierarchical games (1)
  - 91Bxx Mathematical economics (19)
    - 91B08 Individual preferences (2)
    - 91B28 Finance, portfolios, investment (7)
    - 91B52 Special types of equilibria (1)
    - 91B60 General economic models, trade models (4)
    - 91B62 Dynamic economic models, growth models (1)
    - 91B66 Multisectoral models (1)
    - 91B68 Matching models (2)
    - 91B74 Models of real-world systems (1)
    - 91B82 Statistical methods; economic indices and measures (4)
    - 91B84 Economic time series analysis (4)
  - 91Cxx Social and behavioral sciences - methodology (1)
    - 91C20 Clustering (1)
  - 91Fxx Other social and behavioral sciences (mathematical treatment) (1)
    - 91F99 None of the above, but in this section (1)
- 92-XX Biology and other natural sciences (29)
  - 92-08 Computational methods (8)
  - 92Bxx Mathematical biology in general (9)
    - 92B05 General biology and biomathematics (9)
    - 92B99 None of the above, but in this section (1)
  - 92Cxx Physiological, cellular and medical topics (3)
    - 92C37 Cell biology (1)
    - 92C40 Biochemistry, molecular biology (2)
  - 92Dxx Genetics and population dynamics (11)
    - 92D20 Protein sequences, DNA sequences (7)
    - 92D25 Population dynamics (general) (3)
    - 92D30 Epidemiology (1)
- 93-XX Systems theory; control (6)
  - 93Bxx Controllability, observability, and system structure (1)
    - 93B15 Realizations from input-output data (1)
  - 93Cxx Control systems, guided systems (2)
    - 93C55 Discrete-time systems (1)
    - 93C65 Discrete event systems (1)
  - 93Dxx Stability (1)
    - 93D15 Stabilization of systems by feedback (1)
  - 93Exx Stochastic systems and control (2)
    - 93E99 None of the above, but in this section (2)
- 94-XX Information and communication, circuits (12)
  - 94Axx Communication, information (8)
    - 94A05 Communication theory (1)
    - 94A15 Information theory, general (2)
    - 94A60 Cryptography (3)
    - 94A99 None of the above, but in this section (2)
  - 94Cxx Circuits, networks (5)
    - 94C10 Switching theory, application of Boolean algebra; Boolean functions (2)
    - 94C15 Applications of graph theory (2)
    - 94C99 None of the above, but in this section (1)
- 97-XX Mathematics education (1)
  - 97Uxx Educational material and media. Educational technology (1)

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