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Coalgebras and bialgebras in combinatorics.(English)Zbl 0471.05020


MSC:

05E15 Combinatorial aspects of groups and algebras (MSC2010)
05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
16T10 Bialgebras
16T15 Coalgebras and comodules; corings
16T30 Connections of Hopf algebras with combinatorics
06A11 Algebraic aspects of posets

Cite

References:

[1]Rota, On the foundations of combinatorial theory I:, Theory of Möbius functions, Z. Wahrscheinlichkeistheorie 2: pp 340– (1964) ·Zbl 0121.02406 ·doi:10.1007/BF00531932
[2]Mullin, On the foundations of combinatorial theory theory III: Theory of binomial enumeration, Graph Theory Appl. 168 (1970) ·Zbl 0259.12001
[3]Rota, Finite operator calculus, J. Math. Anal. Appl. 42: pp 685– (1973) ·Zbl 0267.05004 ·doi:10.1016/0022-247X(73)90172-8
[4]Doubilet, Sixth Berkeley Symposium on Mathematical Statistics and Probability 2 pp 267– (1972) ·Zbl 0274.05008
[5]Roman, The umbral calculus, Advances in Math. 27(2): pp 95– (1978) ·Zbl 0375.05007 ·doi:10.1016/0001-8708(78)90087-7
[7]Bjorken, Relativistic Quantum Mechanics (1964)
[8]Bourbaki, Algebra (1970)
[9]Crapo, Combinatorial Geometries (1971)
[10]Dieudonné, Introduction to the Theory of Formal Groups (1973)
[11]Doubilet, Ph.D. thesis (1974)
[12]Feinberg, Ph.D. thesis (1974)
[13]Fillmore, A linear algebra setting for the Mullin-Rota theory of polynomials of binomial type, Linear and Multilinear Algebra 1: pp 67– (1973) ·Zbl 0279.05003 ·doi:10.1080/03081087308817006
[14]Garsia, An expose of the Mullin-Rota theory of polynomials of binomial type, Linear and Multilinear Algebra 1: pp 43– (1973) ·Zbl 0287.05008 ·doi:10.1080/03081087308817005
[15]Garsia, A new expression for umbral operators and power series inversion, Proc. Amer. Math. Soc. 64 pp 179– (1977) ·Zbl 0376.05003 ·doi:10.1090/S0002-9939-1977-0444487-4
[16]Goldman, On the foundations of combinatorial theory IV: Finite vector spaces and Eulerian generating functions, Studies in Appl. Math. XLIX (3): pp 239– (1970) ·Zbl 0212.03303 ·doi:10.1002/sapm1970493239
[17]Henle, Binomial enumeration on dissects, Trans. Amer. Math. Soc. 202: pp 1– (1975) ·Zbl 0303.05013 ·doi:10.1090/S0002-9947-1975-0357133-8
[18]Joni, Ph.D. thesis (1977)
[19]Joni, Antipodes and inversion of formal series, J. Algebra (1979)
[21]Leroux, Les categories de Mobius, Cahiers Topologie Gom. Differentielle XVI (3) pp 280– (1975)
[22]Liu, Topics in Combinatorial Mathematics (1972)
[23]Polya, Picture writing, Amer. Math. Monthly 63: pp 689– (1956) ·Zbl 0074.25005 ·doi:10.2307/2309555
[25]Rota, Enumeration under group action, Annali Scuola Norm. Sup. Ser. IV IV: pp 637– (1977) ·Zbl 0367.05008
[26]Schubert, Categories (1972) ·doi:10.1007/978-3-642-65364-3
[27]Sweedler, Hopf Algebras (1969)
[28]Tutte, On dichromatic polynomials, J. Combinatorial Theory 2: pp 301– (1967) ·Zbl 0147.42902 ·doi:10.1016/S0021-9800(67)80032-2
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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