Combinatorics: Combinatorics

• General reference works (handbooks, dictionaries, bibliographies, etc.)
• Instructional exposition (textbooks, tutorial papers, etc.)
• Research exposition (monographs, survey articles)
• Historical (must also be assigned at least one classification number from Section 01)
• Explicit machine computation and programs (not the theory of computation or programming)
• Proceedings, conferences, collections, etc.
• Enumerative combinatorics
• Combinatorial choice problems (subsets, representatives, permutations)
• Factorials, binomial coefficients, combinatorial functions
• Exact enumeration problems, generating functions
• Asymptotic enumeration
• Partitions of integers
• Partitions of sets
• Combinatorial identities
• Combinatorial inequalities
• $q$-calculus and related topics
• Umbral calculus
• None of the above, but in this section
• Designs and configurations
• Block designs
• Triple systems
• Difference sets (number-theoretic, group-theoretic, etc.)
• Orthogonal arrays, Latin squares, Room squares
• Matrices (incidence, Hadamard, etc.)
• Finite geometries
• Other designs, configurations
• Matroids, geometric lattices
• Packing and covering
• Tessellation and tiling problems
• Polyominoes
• None of the above, but in this section
• Graph theory
• Trees
• Degree sequences
• Topological graph theory, imbedding
• Distance in graphs
• Coloring of graphs and hypergraphs
• Perfect graphs
• Directed graphs (digraphs), tournaments
• Signed, gain and biased graphs
• Graphs and groups
• Enumeration of graphs and maps
• Extremal problems
• Paths and cycles
• Connectivity
• Eulerian and Hamiltonian graphs
• Graphs and matrices
• Generalized Ramsey theory
• Isomorphism problems (reconstruction conjecture, etc.)
• Graph representations (geometric and intersection representations, etc.)
• Hypergraphs
• Dominating sets, independent sets, cliques
• Factorization, matching, covering and packing
• Structural characterization of types of graphs
• Graph labelling (graceful graphs, bandwidth, etc.)
• Random graphs
• Graph minors
• Graph algorithms
• Applications
• None of the above, but in this section
• Extremal combinatorics
• Extremal set theory
• Ramsey theory
• Transversal (matching) theory
• Probabilistic methods
• None of the above, but in this section
• Algebraic combinatorics
• Symmetric functions
• Tableaux, representations of the symmetric group
• Combinatorial problems concerning the classical groups
• Group actions on designs, geometries and codes
• Group actions on posets and homology groups of posets
• Association schemes, strongly regular graphs
• Orthogonal polynomials
• None of the above, but in this section