05A05 Combinatorial choice problems (subsets, representatives, permutations)
05A10 Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx]
05A15 Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
05A16 Asymptotic enumeration
05A17 Partitions of integers [See also 11P81, 11P82, 11P83]
05A18 Partitions of sets
05A19 Combinatorial identities
05A20 Combinatorial inequalities
05A30 q-calculus and related topics [See also 03Dxx]
05A40 Umbral calculus
05A99 None of the above, but in this section

05B05 Block designs [See also 51E05, 62K10]
05B07 Triple systems
05B10 Difference sets (number-theoretic, grouptheoretic, etc.) [See also 11B13]
05B15 Orthogonal arrays, Latin squares, Room squares
05B20 Matrices (incidence, Hadamard, etc.)
05B25 Finite geometries [See also 51D20, 51Exx]
05B30 Other designs, configurations [See also 51E30]
05B35 Matroids, geometric lattices [See also 52B40, 90C27]
05B40 Packing and covering [See also 11H31, 52C15, 52C17]
05B45 Tessellation and tiling problems [See also 52C20, 52C22]
05B50 Polyominoes 05B99 None of the above, but in this section

05C05 Trees
05C07 Degree sequences
05C10 Topological graph theory, imbedding [See also 57M15, 57M25]
05C12 Distance in graphs
05C15 Coloring of graphs and hypergraphs
05C17 Perfect graphs
05C20 Directed graphs (digraphs), tournaments
05C22 Signed, gain and biased graphs
05C25 Graphs and groups [See also 20F65]
05C30 Enumeration of graphs and maps
05C35 Extremal problems [See also 90C35]
05C38 Paths and cycles [See also 90B10]
05C40 Connectivity
05C45 Eulerian and Hamiltonian graphs
05C50 Graphs and matrices
05C55 Generalized Ramsey theory
05C60 Isomorphism problems (reconstruction conjecture, etc.)
05C62 Graph representations (geometric and intersection representations, etc.)
05C65 Hypergraphs
05C69 Dominating sets, independent sets, cliques
05C70 Factorization, matching, covering and packing
05C75 Structural characterization of types of graphs
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C80 Random graphs
05C83 Graph minors
05C85 Graph algorithms [See also 68R10, 68W05]
05C90 Applications
05C99 None of the above, but in this section

05D05 Extremal set theory
05D10 Ramsey theory
05D15 Transversal (matching) theory
05D40 Probabilistic methods
05D99 None of the above, but in this section

05E05 Symmetric functions
05E10 Tableaux, representations of the symmetric group [See also 20C30]
05E15 Combinatorial problems concerning the classical groups [See also 22E45, 33C80]
05E20 Group actions on designs, geometries and codes
05E25 Group actions on posets and homology groups of posets [See also 06A11]
05E30 Association schemes, strongly regular graphs
05E35 Orthogonal polynomials [See also 33C45, 33C50, 33D45]
05E99 None of the above, but in this section

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05-XX COMBINATORICS {For finite fields, see 11Txx}
05-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
05-01 Instructional exposition (textbooks, tutorial papers, etc.)
05-02 Research exposition (monographs, survey articles)
05-03 Historical (must also be assigned at least one classification number from Section 01)
05-04 Explicit machine computation and programs (not the theory of computation or programming)
05-06 Proceedings, conferences, collections, etc.

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This is a completely revised version of the MSC, prepared collaboratively in the editorial offices of MR and Zentralblatt MATH. It replaces the 1991 MSC and is effective (in MR) with the January 2000 issue (2000a).

While in many areas in the MSC there are only very small changes, others have been expanded significantly, and in some areas there is an altogether new classification. The major changes are as follows: Section 04 has been eliminated; 03E will now be used for items previously classified in 04. A new section, 37, has been created for Dynamical systems and ergodic theory; as a result Section 58F has been eliminated. Also in Section 58, 58G has been completely revised and now appears as 58J. The new Section 74, Mechanics of deformable solids, is a completely revised version of Section 73, which has been eliminated. The areas covered by Sections 90 and 92 have been reorganized into Sections 90, 91 and 92. Sections 90B and 90C remain essentially unchanged. The new Section 91A replaces 90D and 91B replaces 90A. The other subsections of 91 replace the old subsections 92G, H, J and K. Sections 92B, C, D, and E remain essentially unchanged. MSC2000 contains a new section, 97, for Mathematics education. This will be used only as a secondary classification in MR. Other sections with significant additions or reorganization include 14, 22, 32, 34, 46, 47, 53, and 65.

To help users of the MSC, conversion tables have been constructed and are available on the AMS web site, www.ams.org. These give, for each 1991 classification that does not appear in MSC2000, the classification(s) in MSC2000 that are most likely to be used for items that would previously have been classified using the old classification, and, for each new classification in MSC2000, the classification(s) in the 1991 MSC that are most likely to have been used earlier for items classified using the new classification.

Instructions for using the Mathematics Subject Classification 2000

These instructions apply uniformly to all fields listed. The main purpose of the classification is to help readers find the items of present or potential interest to them as readily as possible-- in MR, in Zbl, or anywhere else where this classification system

is used. A paper or book should be listed under the classification where it will receive the broadest attention from readers possibly interested in it--these include both people working in that area and people who are familiar with that area and apply its results and methods elsewhere (inside or outside mathematics). It will be extremely useful for both readers and classifiers to familiarize themselves with the entire classification system and thus to become aware of all the classifications of possible interest to them.

For every paper or book listed, MR chooses precisely one "primary" classification, which is simply the code for the section (MSC entry) in which the item will be located. This section should be the one that covers the principal contribution. When an item contains several principal contributions in different areas, the primary classification should cover the "most important" among them. A paper or book may receive one or several "secondary" classifications (or "cross-references") to cover any remaining principal contributions, ancillary results, motivation or origin of the problems discussed, intended or potential field of application, or other significant aspects worthy of notice.

The "primary" principal contribution is meant to be the one including the most important part of the work actually done in the item under consideration. For example, a paper whose main overall content is the solution of a problem in graph theory, which arose in computer science and whose solution is, say, at present only of interest to computer scientists, belongs primarily in 05C with a cross-reference in 68; conversely, a paper whose overall content lies mainly in computer science should receive a primary classification in 68, even if it makes heavy use of graph theory and proves several new graph-theoretic results along the way.

There are two types of cross-references given after many classifications in the list. The first type is of the form "{For A, see X}"; if this appears in section Y, it means that for contributions described by A one should usually assign the classification X, not Y. The other type of cross-reference merely points out related classifications; it is of the form "[See also . . . ]", "[See mainly . . . ]", etc., and the classifications listed in the brackets may, but need not, be added to the classification of a paper, or they may be used in place of the classification where the cross-reference is given. The classifier will have to judge which classification is the most appropriate for the item at hand.