3,078 research outputs found
Balanced supersaturation for some degenerate hypergraphs
A classical theorem of Simonovits from the 1980s asserts that every graph
satisfying must contain copies of . Recently, Morris and
Saxton established a balanced version of Simonovits' theorem, showing that such
has copies of , which
are `uniformly distributed' over the edges of . Moreover, they used this
result to obtain a sharp bound on the number of -free graphs via the
container method. In this paper, we generalise Morris-Saxton's results for even
cycles to -graphs. We also prove analogous results for complete
-partite -graphs.Comment: Changed title, abstract and introduction were rewritte
A local homology theory for linearly compact modules
We introduce a local homology theory for linearly compact modules which is in
some sense dual to the local cohomology theory of A. Grothendieck. Some basic
properties such as the noetherianness, the vanishing and non-vanishing of local
homology modules of linearly compact modules are proved. A duality theory
between local homology and local cohomology modules of linearly compact modules
is developed by using Matlis duality and Macdonald duality. As consequences of
the duality theorem we obtain some generalizations of well-known results in the
theory of local cohomology for semi-discrete linearly compact modules.Comment: 24 page
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