Geodesic
Invariants of symmetric and alternating groups
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 201-210

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A theorem is proved on the growth of the codimension and the defect of the algebras of the invariants of symmetric and alternating groups with the growth of the dimension of the representations without trivial components, containing irreducible, non-one-dimensional, nonstandard subrepresentations. 
@article{ZNSL_1987_160_a18,
     author = {N. L. Gordeev},
     title = {Invariants of symmetric and alternating groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {201--210},
     publisher = {mathdoc},
     volume = {160},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a18/}
}
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N. L. Gordeev. Invariants of symmetric and alternating groups. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 201-210. http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a18/