Profitability Study of MPAA Rated Movies

Concerned with the limited number of family oriented films currently produced each year and an increase in the number of films containing sex and violence, The Dove Foundation is interested in determining which films, by MPAA rating, produce the greatest profits as well as the highest rates of return on investment (ROI)

On a curious variant of the SnS_n-module LienLie_n

We introduce a variant of the much-studied $Lie$ representation of the symmetric group $S_n$, which we denote by $Lie_n^{(2)}.$ Our variant gives rise to a decomposition of the regular representation as a sum of {exterior} powers of modules $Lie_n^{(2)}.$ This is in contrast to the theorems of Poincar\'e-Birkhoff-Witt and Thrall which decompose the regular representation into a sum of symmetrised $Lie$ modules. We show that nearly every known property of $Lie_n$ has a counterpart for the module $Lie_n^{(2)},$ suggesting connections to the cohomology of configuration spaces via the character formulas of Sundaram and Welker, to the Eulerian idempotents of Gerstenhaber and Schack, and to the Hodge decomposition of the complex of injective words arising from Hochschild homology, due to Hanlon and Hersh.Comment: 26 pages, 2 tables. To appear in Algebraic Combinatorics. Parts of this paper are included in arXiv:1803.0936

The Employment-Unemployment Situation in India in the Nineteen Nineties: Some Results from the NSS 55th Round Survey (July 1999-June 2000)

Based on a comparative analysis of the NSS Employment-Unemployment Surveys for 1993-94 and 1999-2000, this paper examines, at the all-India level, the changes in: the size and structure of workforce; the extent of unemployment and under employment; in labour productivity and days worked; and, in wage earnings per worker and per head of population in rural and urban India. Key results include, a slower growth of work force relative to that of population, a reduction in the share and size of the work force in agriculture and in community, social and personal services; and, widespread gains in labour productivity getting translated into equally widespread and significant growth in average wage earnings per worker and per capita.