zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the foundations of combinatorial theory. I: Theory of Möbius functions. (English) Zbl 0121.02406

References:
[1]Auslander, L., and H. M. Trent: Incidence matrices and linear graphs. J. Math. Mech. 8, 827-835 (1959).
[2]Bell, E. T.: Algebraic Arithmetic. New York: Amer. Math. Soc. (1927),
[3]?: Exponential polynomials. Ann. of Math., II. Ser. 35, 258-277 (1934). · doi:10.2307/1968431
[4]Berge, C.: Théorie des graphes et ses applications. Paris: Dounod 1958.
[5]Birkhoff, Garrett: Lattice Theory, third preliminary edition. Harvard University, 1963.
[6]- Lattice Theory, revised edition. American Mathematical Society, 1948.
[7]Birkhoff, G. D.: A determinant formula for the number of ways of coloring a map. Ann. of Math., II. Ser. 14, 42-46 (1913). · doi:10.2307/1967597
[8]?, and D. C. Lewis: Chromatic polynomials. Trans. Amer. math. Soc. 60, 355-451 (1946).
[9]Bleicher, M. N., and G. B. Preston: Abstract linear dependence relations. Publ. Math., Debrecen 8, 55-63 (1961).
[10]Bougayev, N. V.: Theory of numerical derivatives. Moscow, 1870-1873, pp. 1-222.
[11]Bruijn, N. G. De: Generalization of Polya’s fundamental theorem in enumerative combinatorial analysis. Indagationes math. 21, 59-69 (1959).
[12]Chung, K.-L., and L. T. C. Hsu: A combinatorial formula with its application to the theory of probability of arbitrary events. Ann. math. Statistics 16, 91-95 (1945). · Zbl 0060.28310 · doi:10.1214/aoms/1177731175
[13]Dedekind, R.: Gesammelte Mathematische Werke, volls. I?II?III. Hamburg: Deutsche Math. Verein. (1930).
[14]Delsarte, S.: Fonctions de Möbius sur les groupes abéliens finis. Ann. of Math., II. Ser. 49, 600-609 (1948). · Zbl 0031.34102 · doi:10.2307/1969047
[15]Dilworth, R. P.: Proof of a conjecture on finite modular lattices. Ann. of Math., II. Ser. 60, 359-364 (1954). · Zbl 0056.26203 · doi:10.2307/1969639
[16]Dirac, G. A.: On the four-color conjecture. Proc. London math. Society, III. Ser. 13, 193 to 218 (1963).
[17]Dowker, C. H.: Homology groups of relations. Ann. of Math., II. Ser. 56, 84-95 (1952). · Zbl 0046.40402 · doi:10.2307/1969768
[18]Dubreil-Jacotin, M.-L., L. Lesieur et R. Croisot: LeÇons sur la théorie des treilles des structures algebriques ordonnées et des treilles géometriques. Paris: Gauthier-Villars 1953.
[19]Eilenberg, S., and N. Steenrod: Foundations of algebraic topology. Princeton: University Press 1952.
[20]Fary, I.: On straight-line representation of planar graphs. Acta Sci. math. Szeged 11, 229-233 (1948).
[21]Feller, W.: An introduction to probability theory and its applications, second edition. New York: Wiley 1960.
[22]Franklin, P.: The four-color problem. Amer. J. Math. 44, 225-236 (1922). · Zbl 02602337 · doi:10.2307/2370527
[23]Fréchet, M.: Les probabilités associées à un système d’événements compatibles et dépendants. Actualitées scientifiques et industrielles, nos. 859 et 942. Paris: Hermann 1940 et 1943.
[24]Frontera Marqués, B.: Una función numérica en los retículos finitos que se anula para los retícules reducibles. Actas de la 2a, Reunión de matemáticos españoles. Zaragoza 103-111 1962.
[25]Frucht, R., and G.-C. Rota: La función de Möbius para el retículo di particiones de un conjunto finito. To appear in Scientia (Chile).
[26]Goldberg, K., M. S. Green and R. E. Nettleton: Dense subgraphs and connectivity. Canadian J. Math. 11 (1959).
[27]Golomb, S. W.: A mathematical theory of discrete classification. Fourth Symposium in Information Theory, London, 1961.
[28]Green, M. S., and R. E. Nettleton: Möbius function on the lattice of dense subgraphs. J. Res. nat. Bur. Standards 64B, 41-47 (1962).
[29]? ?: Expression in terms of modular distribution functions for the entropy density in an infinite system. J. Chemical Physisc 29, 1365-1370 (1958). · doi:10.1063/1.1744724
[30]Hadwiger, H.: Eulers Charakteristik und kombinatorische Geometrie. J. reine angew. Math. 194, 101-110 (1955). · Zbl 0064.16602 · doi:10.1515/crll.1955.194.101
[31]Hall, Philip: A contribution to the theory of groups of prime power order. Proc. London math. Soc., II. Ser. 36, 39-95 (1932).
[32]- The Eulerian functions of a group. Quart. J. Math. Oxford Ser. 134-151, 1936.
[33]Harary, F.: Unsolved problems in the enumeration of graphs. Publ. math. Inst. Hungar. Acad. Sci. 5, 63-95 (1960).
[34]Hardy, G. H.: Ramanujan. Cambridge: University Press 1940.
[35]?, and E. M. Wright: An introduction to the theory of numbers. Oxford: University Press 1954.
[36]Hartmanis, J.: Lattice theory of generalized partitions. Canadian J. Math. 11, 97-106 (1959). · Zbl 0089.37002 · doi:10.4153/CJM-1959-013-8
[37]Hille, E.: The inversion problems of Möbius. Duke math. J. 3, 549-568 (1937). · doi:10.1215/S0012-7094-37-00344-2
[38]Hsu, L. T. C.: Abstract theory of inversion of iterated summation. Duke math. J. 14, 465 to 473 (1947). · Zbl 0030.11003 · doi:10.1215/S0012-7094-47-01438-5
[39]?: On Romanov’s device of orthogonalization. Sci. Rep. Nat. Tsing Hua Univ. 5, 1-12 (1948).
[40]?: Note on an abstract inversion principle. Proc. Edinburgh math. Soc. (2) 9, 71-73 (1954). · Zbl 0058.02402 · doi:10.1017/S0013091500021313
[41]Jackson, F. H.: Series connected with the enumeration of partitions. Proc. London math. Soc., II. Ser. 1, 63-88 (1904). · doi:10.1112/plms/s2-1.1.63
[42]?: The q-form of Taylor’s theorem. Messenger of Mathematics 38, 57-61 (1909).
[43]Jónsson, B.: Lattice-theoretic approach to projective and affine geometry. Symposium on the Axiomatic Method. Amsterdam, North-Holland Publishing Company, 1959, 188-205.
[44]?, and A. Tarski: Direct decomposition of finite algebraic systems. Notre Dame Mathematical lectures, no. 5. Indiana: Notre Dame 1947.
[45]Kac, M., and J. C. Ward: A combinatorial solution of the two-dimensional Ising model. Phys. Review 88, 1332-1337 (1952). · Zbl 0048.45804 · doi:10.1103/PhysRev.88.1332
[46]Kaplanski, I., and J. Riordan: The problème des ménages. Scripta math. 12, 113-124 (1946).
[47]Klee, V.: The Euler characteristic in combinatorial geometry. Amer. math. Monthly 70, 119-127 (1963). · Zbl 0124.37802 · doi:10.2307/2312880
[48]Lazarson, T.: The representation problem for independence functions. J. London math. Soc. 33, 21-25 (1958). · Zbl 0083.00403 · doi:10.1112/jlms/s1-33.1.21
[49]MacLane, S.: A lattice formulation of transcendence degrees and p-bases. Duke math. J. 4, 455-468 (1938). · doi:10.1215/S0012-7094-38-00438-7
[50]MacMillan, B.: Absolutely monotone functions. Ann. of Math., II. Ser. 60, 467-501 (1954). · Zbl 0057.29002 · doi:10.2307/1969847
[51]Möbius, A. F.: über eine besondere Art von Umkehrung der Reihen. J. reine angew. Math. 9, 105-123 (1832). · Zbl 02751479 · doi:10.1515/crll.1832.9.105
[52]Ore, O.: Theory of graphs. Providence: American Mathematical Society 1962.
[53]Polya, G.: Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen. Acta math. 68, 145-253 (1937). · Zbl 0017.23202 · doi:10.1007/BF02546665
[54]Rado, R.: Note on independence functions. Proc. London math. Soc., III. Ser. 7, 300-320 (1957). · Zbl 0083.02302 · doi:10.1112/plms/s3-7.1.300
[55]Read, R. C.: The enumeration of locally restricted graphs, I. J. London math. Soc. 34, 417 to 436 (1959).
[56]Redfield, J. H.: The theory of group-reduced distributions. Amer. J. Math. 49, 433-455 (1927). · Zbl 02581107 · doi:10.2307/2370675
[57]Revuz, André: Fonctions croissantes et mesures sur les espaces topologiques ordonnés. Ann. Inst. Fourier 6 187-268 (1955).
[58]Riordan, J.: An introduction to combinatorial analysis. New York: Wiley 1958.
[59]Romanov, N. P.: On a special orthonormal system and its connection with the theory of primes. Math. Sbornik, N. S. 16, 353-364 (1945).
[60]Rota, G.-C.: Combinatorial theory and Möbius functions. To appear in Amer. math. Monthly.
[61]- The number of partitions of a set. To appear in Amer. math. Monthly.
[62]Ryser, H. J.: Combinatorial Mathematics. Buffalo: Mathematical Association of America 1963.
[63]Schützenberger, M. P.: Contribution aux applications statistiques de la théorie de l’information. Publ. Inst. Stat. Univ. Paris, 3, 5-117 (1954).
[64]Tarski, A.: Ordinal algebras. Amsterdam: North-Holland Publishing Company 1956.
[65]Touchard, J.: Sur un problème de permutations. C. r. Acad. Sci., Paris, 198, 631-633 (1934).
[66]Tutte, W. T.: A contribution to the theory of chromatic polynomials. Canadian J. Math. 6, 80-91 (1953). · Zbl 0055.17101 · doi:10.4153/CJM-1954-010-9
[67]?: A class of Abelian group. Canadian J. Math. 8, 13-28 (1956). · Zbl 0070.02302 · doi:10.4153/CJM-1956-004-9
[68]?: A homotopy theorem for matroids, I. and II. Trans. Amer. math. Soc. 88, 144-140 (1958).
[69]?: Matroids and graphs. Trans. Amer. math. Soc. 90, 527-552 (1959). · doi:10.1090/S0002-9947-1959-0101527-3
[70]Ward, M.: The algebra of lattice functions. Duke math. J. 5, 357-371 (1939). · doi:10.1215/S0012-7094-39-00531-4
[71]Weisner, L.: Abstract theory of inversion of finite series. Trans. Amer. math. Soc. 38, 474-484 (1935). · doi:10.1090/S0002-9947-1935-1501822-0
[72]?: Some properties of prime-power groups. Trans. Amer. math. Soc. 38, 485-492 (1935). · doi:10.1090/S0002-9947-1935-1501823-2
[73]Whitney, H.: A logical expansion in mathematics. Bull. Amer. math. Soc. 38, 572-579 (1932). · doi:10.1090/S0002-9904-1932-05460-X
[74]?: Characteristic functions and the algebra of logic. Ann. of Math., II. Ser. 34, 405-414 (1933). · doi:10.2307/1968168
[75]?: The abstract properties of linear dependence. Amer. J. Math. 57, 507-533 (1935). · doi:10.2307/2371182
[76]Wielandt, H.: Beziehungen zwischen den Fixpunktzahlen von Automorphismengruppen einer endliehen Gruppe. Math. Z. 73, 146-158 (1960). · Zbl 0093.02302 · doi:10.1007/BF01162475
[77]Wintner, A.: Eratosthenian Averages. Baltimore (privately printed) 1943.