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Volumn 124, Issue 2, 1996, Pages 207-271

The umbral calculus of symmetric functions

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EID: 0030602324     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1996.0083     Document Type: Article
Times cited : (6)

References (48)
  • 1
    • 49049134465 scopus 로고
    • Recursive methods and the umbral calculus
    • 1. M. Barnabei, A. Brini, and G. Nicoletti, Recursive methods and the umbral calculus, J. Algebra 75 (1982), 549-573.
    • (1982) J. Algebra , vol.75 , pp. 549-573
    • Barnabei, M.1    Brini, A.2    Nicoletti, G.3
  • 2
    • 0011525953 scopus 로고
    • A general umbral calculus in infinitely many variables
    • 2. M. Barnabei, A. Brini, and G. Nicoletti, A general umbral calculus in infinitely many variables, Adv. Math. 50 (1983), 49-93.
    • (1983) Adv. Math. , vol.50 , pp. 49-93
    • Barnabei, M.1    Brini, A.2    Nicoletti, G.3
  • 3
    • 33748725707 scopus 로고
    • Une combinatoire du pléthysme
    • 3. F. Bergeron, Une combinatoire du pléthysme, J. Combin. Theory Ser. A 46 (1987), 291-305.
    • (1987) J. Combin. Theory Ser. A , vol.46 , pp. 291-305
    • Bergeron, F.1
  • 4
    • 38249024944 scopus 로고
    • A new class of symmetric polynomials defined in terms of tableaux
    • 4. L. Biederharn and J. Louck, A new class of symmetric polynomials defined in terms of tableaux, Adv. Appl. Math. 10 (1989), 396-438.
    • (1989) Adv. Appl. Math. , vol.10 , pp. 396-438
    • Biederharn, L.1    Louck, J.2
  • 5
    • 0025091839 scopus 로고
    • Inhomogeneous basis set of symmetric polynomials defined by tableaux
    • 5. L. Biederharn and J. Louck, Inhomogeneous basis set of symmetric polynomials defined by tableaux, Proc. Natl. Acad. Sci. U.S.A. 87 (1990) 1441-1445.
    • (1990) Proc. Natl. Acad. Sci. U.S.A. , vol.87 , pp. 1441-1445
    • Biederharn, L.1    Louck, J.2
  • 9
    • 0000039097 scopus 로고
    • Compositional calculus
    • 9. W. Chen, Compositional calculus, J. Combin. Theory Ser. A 64 (1993), 149-188.
    • (1993) J. Combin. Theory Ser. A , vol.64 , pp. 149-188
    • Chen, W.1
  • 10
    • 0002878758 scopus 로고
    • The theory of compositionals
    • 10. W. Chen, The theory of compositionals, Discrete Math. 122 (1993), 58-97.
    • (1993) Discrete Math. , vol.122 , pp. 58-97
    • Chen, W.1
  • 11
    • 21144470953 scopus 로고
    • The factorial Schur function
    • 11. W. Chen and J. Louck, The factorial Schur function, J. Math. Phys. 34 (1993), 4144-4160.
    • (1993) J. Math. Phys. , vol.34 , pp. 4144-4160
    • Chen, W.1    Louck, J.2
  • 12
    • 0011590574 scopus 로고
    • On combinatorial structures kept fixed by the action of a given permutation
    • 12. I. Constantineau and J. Labelle, On combinatorial structures kept fixed by the action of a given permutation, Stud. Appl. Math. 84 (1991), 105-118.
    • (1991) Stud. Appl. Math. , vol.84 , pp. 105-118
    • Constantineau, I.1    Labelle, J.2
  • 13
    • 0001254907 scopus 로고
    • On the foundations of combinatorial theory. VII. Symmetric functions through the theory of distributions and occupancy
    • 13. P. Doubilet, On the foundations of combinatorial theory. VII. Symmetric functions through the theory of distributions and occupancy, Stud. Appl. Math. 51 (1972), 377-396.
    • (1972) Stud. Appl. Math. , vol.51 , pp. 377-396
    • Doubilet, P.1
  • 14
    • 0011525633 scopus 로고
    • On D. E. Littlewood's algebra of S-functions
    • 14. D. G. Duncan, On D. E. Littlewood's algebra of S-functions, Can. J. Math. 4 (1952), 504-512.
    • (1952) Can. J. Math. , vol.4 , pp. 504-512
    • Duncan, D.G.1
  • 15
    • 0002448055 scopus 로고
    • A combinatorial interpretation of the inverse Kostka matrix
    • 15. O. Egecioglu and J. B. Remmel, A combinatorial interpretation of the inverse Kostka matrix, Linear and Multilinear Algebra 26 (1990), 59-84.
    • (1990) Linear and Multilinear Algebra , vol.26 , pp. 59-84
    • Egecioglu, O.1    Remmel, J.B.2
  • 16
    • 38149147343 scopus 로고
    • A bijective proof of infinite variated Good's inversion
    • 16. R. Ehrenborg and M. Méndez, A bijective proof of infinite variated Good's inversion, Adv. Math. 103 (1994), 221-259.
    • (1994) Adv. Math. , vol.103 , pp. 221-259
    • Ehrenborg, R.1    Méndez, M.2
  • 18
    • 38249034240 scopus 로고
    • A combinatorial proof of the multivariable Lagrange inversion formula
    • 18. I. M. Gessel, A combinatorial proof of the multivariable Lagrange inversion formula, J. Combin. Theory Ser. A 45 (1987), 178-195.
    • (1987) J. Combin. Theory Ser. A , vol.45 , pp. 178-195
    • Gessel, I.M.1
  • 19
    • 0002827141 scopus 로고
    • Lagrange inversion for species
    • 19. I. M. Gessel and G. Labell, Lagrange inversion for species, J. Combin. Theory 72 (1995), 95-117.
    • (1995) J. Combin. Theory , vol.72 , pp. 95-117
    • Gessel, I.M.1    Labell, G.2
  • 21
    • 84971179361 scopus 로고
    • Generalizations to several variables of Lagrange's expansion with applications to stocastic processes
    • 21. I. J. Good, Generalizations to several variables of Lagrange's expansion with applications to stocastic processes, Proc. Cambridge Philos. Soc. 56 (1960), 367-380.
    • (1960) Proc. Cambridge Philos. Soc. , vol.56 , pp. 367-380
    • Good, I.J.1
  • 22
    • 0011526236 scopus 로고
    • Shift operators and factorial symmetric functions
    • 22. I. P. Goulden and A. M. Hamel, Shift operators and factorial symmetric functions, J. Combin. Theory Ser. A 69 (1995), 51-60.
    • (1995) J. Combin. Theory Ser. A , vol.69 , pp. 51-60
    • Goulden, I.P.1    Hamel, A.M.2
  • 23
    • 0011587675 scopus 로고
    • A cycle index sum inversion theorem
    • 23. P. Hanlon. A cycle index sum inversion theorem, J. Combin. Theory Ser. A 30 (1981), 248-269.
    • (1981) J. Combin. Theory Ser. A , vol.30 , pp. 248-269
    • Hanlon, P.1
  • 24
    • 0000059567 scopus 로고
    • Lagrange inversion in higher dimensions and umbral operators
    • 24. S. A. Joni, Lagrange inversion in higher dimensions and umbral operators, Linear and Multilinear Algebra 6 (1978), 111-121.
    • (1978) Linear and Multilinear Algebra , vol.6 , pp. 111-121
    • Joni, S.A.1
  • 26
    • 0002738602 scopus 로고
    • Coalgebras and bialgebras in combinatorics
    • 26. S. A. Joni and G.-C. Rota, Coalgebras and bialgebras in combinatorics, Stud. Appl. Math. 61 (1979), 93-139.
    • (1979) Stud. Appl. Math. , vol.61 , pp. 93-139
    • Joni, S.A.1    Rota, G.-C.2
  • 28
    • 0011588527 scopus 로고
    • Quotienten und kerne von young-diagrammen, brettspiele und plethysmen gewöhnlicher irreduzibler darstellungen symmetrischer gruppen
    • 28. A. Kerber, F. Sänger, and B. Wagner, Quotienten und Kerne von Young-Diagrammen, Brettspiele und Plethysmen gewöhnlicher irreduzibler Darstellungen symmetrischer Gruppen, Mitt. Math. Sem. Gessen 149 (1981), 131-175.
    • (1981) Mitt. Math. Sem. Gessen , vol.149 , pp. 131-175
    • Kerber, A.1    Sänger, F.2    Wagner, B.3
  • 30
    • 0038336010 scopus 로고
    • Wronski's factorization of polynomials
    • part 2, PWN Polish Scientific Publishers, Warsaw
    • 30. A. Lascoux, Wronski's factorization of polynomials, in "Topics in Algebra, Banach Center Publications," Vol. 26, part 2, PWN Polish Scientific Publishers, Warsaw, 1990.
    • (1990) Topics in Algebra, Banach Center Publications , vol.26
    • Lascoux, A.1
  • 31
    • 0011525954 scopus 로고
    • Sequences of symmetric functions of binomial type
    • 31. D. Loeb, Sequences of symmetric functions of binomial type, Stud. Appl. Math. 81 (1990), 1-30.
    • (1990) Stud. Appl. Math. , vol.81 , pp. 1-30
    • Loeb, D.1
  • 34
    • 0004205063 scopus 로고
    • Cambridge Univ. Press, reprinted, Chelsea, New York
    • 34. P. A. MacMahon, "Combinatorial Analysis," Vols. 1, 2, Cambridge Univ. Press, 1915; reprinted, Chelsea, New York, 1960.
    • (1915) Combinatorial Analysis , vol.1-2
    • MacMahon, P.A.1
  • 35
    • 38248999045 scopus 로고
    • Multisets and the combinatorics if symmetric functions
    • 35. M. Méndez, Multisets and the combinatorics if symmetric functions, Adv. Math. 102 (1993), 95-125.
    • (1993) Adv. Math. , vol.102 , pp. 95-125
    • Méndez, M.1
  • 36
    • 0040007912 scopus 로고    scopus 로고
    • Plethystic exponential polynomials and plethystic Stirling numbers
    • 36. A. Méndez, Plethystic exponential polynomials and plethystic Stirling numbers, Stud. Appl. Math.. 96 (1996), 1-8.
    • (1996) Stud. Appl. Math.. , vol.96 , pp. 1-8
    • Méndez, A.1
  • 37
    • 38249000436 scopus 로고
    • Colored species, C-monoids and plethysm, I
    • 37. M. Méndez and O. Nava, Colored species, C-monoids and plethysm, I, J. Combin. Theory Ser. A 64 (1993), 102-128.
    • (1993) J. Combin. Theory Ser. A , vol.64 , pp. 102-128
    • Méndez, M.1    Nava, O.2
  • 39
    • 0002381228 scopus 로고
    • Witt vectors and the algebra of necklaus
    • 39. N. Metropolis and G.-C. Rota, Witt vectors and the algebra of necklaus, Adv. in Math. 50 (1983), 95-125.
    • (1983) Adv. in Math. , vol.50 , pp. 95-125
    • Metropolis, N.1    Rota, G.-C.2
  • 40
    • 0002934845 scopus 로고
    • On the foundations of combinatorial theory. III. Theory of binomial enumeration
    • Academic Press, New York
    • 40. R. Mullin and G.-C. Rota, On the foundations of combinatorial theory. III. Theory of binomial enumeration, in "Graph Theory and Its Applications," pp. 167-213. Academic Press, New York, 1970.
    • (1970) Graph Theory and its Applications , pp. 167-213
    • Mullin, R.1    Rota, G.-C.2
  • 41
    • 0005520948 scopus 로고
    • On the combinatorics of plethysm
    • 41. O. Nava, On the combinatorics of plethysm, J. Combin. Theory Ser. A 46 (1987), 215-251.
    • (1987) J. Combin. Theory Ser. A , vol.46 , pp. 215-251
    • Nava, O.1
  • 42
    • 70349149931 scopus 로고
    • Multivariate sequences of binomial type
    • 42. D. L. Reiner, Multivariate sequences of binomial type, Stud. Appl. Math. 57 (1977), 340-381.
    • (1977) Stud. Appl. Math. , vol.57 , pp. 340-381
    • Reiner, D.L.1
  • 43
    • 0011651461 scopus 로고
    • On symmetric functions related to Witt vectors and Lie algebra
    • 43. C. Reutenauer, On symmetric functions related to Witt vectors and Lie algebra, Adv. in Math. 110 (1995), 234-246.
    • (1995) Adv. in Math. , vol.110 , pp. 234-246
    • Reutenauer, C.1
  • 44
    • 0000214958 scopus 로고
    • The algebra of formal series III: Several variables
    • 44. S. Roman, The algebra of formal series III: Several variables, J. Approx. Theory 26 (1979), 340-381.
    • (1979) J. Approx. Theory , vol.26 , pp. 340-381
    • Roman, S.1
  • 45
    • 0002300455 scopus 로고
    • The umbral calculus
    • 45. S. Roman and G.-C. Rota, The umbral calculus, Adv. in Math. 27 (1978), 95-188.
    • (1978) Adv. in Math. , vol.27 , pp. 95-188
    • Roman, S.1    Rota, G.-C.2
  • 47
    • 0002842550 scopus 로고
    • A Hopf-algebra approach to inner plethysm
    • 47. T. Scharf and J.-Y. Thibon, A Hopf-algebra approach to inner plethysm, Adv. in Math. 104 (1994), 30-58.
    • (1994) Adv. in Math. , vol.104 , pp. 30-58
    • Scharf, T.1    Thibon, J.-Y.2
  • 48
    • 0001452386 scopus 로고
    • A symmetric function generalization of the chromatic polynomial of a graph
    • 48. R. P. Stanley, A symmetric function generalization of the chromatic polynomial of a graph, Adv. in Math. 111 (1995), 166-194.
    • (1995) Adv. in Math. , vol.111 , pp. 166-194
    • Stanley, R.P.1


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