Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Asymptotics (1)
- Bounded point evaluations (1)
- Combinatorics (1)
- Commutative algebra (1)
- Determinants (1)
-
- Discrete Morse Theory (1)
- Group Action (1)
- Homology (1)
- Homotopy (1)
- Lefschetz properties (1)
- Monomial ideals (1)
- Partition Lattice (1)
- Pattern Avoidance (1)
- Q--capacity (1)
- Representing measures (1)
- Simplicial Complex (1)
- Specht Module (1)
- Spectral Method (1)
- Uniform and Lp rational approximation (1)
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Analytic And Topological Combinatorics Of Partition Posets And Permutations, Jiyoon Jung
Analytic And Topological Combinatorics Of Partition Posets And Permutations, Jiyoon Jung
Theses and Dissertations--Mathematics
In this dissertation we first study partition posets and their topology. For each composition c we show that the order complex of the poset of pointed set partitions is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with descent composition c. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module of a border strip associated to the composition. We also study the filter of pointed set partitions generated by knapsack integer partitions. In the second half of this dissertation we study descent …
Rational Approximation On Compact Nowhere Dense Sets, Christopher Mattingly
Rational Approximation On Compact Nowhere Dense Sets, Christopher Mattingly
Theses and Dissertations--Mathematics
For a compact, nowhere dense set X in the complex plane, C, define Rp(X) as the closure of the rational functions with poles off X in Lp(X, dA). It is well known that for 1 ≤ p < 2, Rp(X) = Lp(X) . Although density may not be achieved for p > 2, there exists a set X so that Rp(X) = Lp(X) for p up to a given number greater than 2 but not after. Additionally, when p > 2 we shall establish that the support of the annihiliating and …
Lefschetz Properties And Enumerations, David Cook Ii
Lefschetz Properties And Enumerations, David Cook Ii
Theses and Dissertations--Mathematics
An artinian standard graded algebra has the weak Lefschetz property if the multiplication by a general linear form induces maps of maximal rank between consecutive degree components. It has the strong Lefschetz property if the multiplication by powers of a general linear form also induce maps of maximal rank between the appropriate degree components. These properties are mainly studied for the constraints they place, when present, on the Hilbert series of the algebra. While the majority of research on the Lefschetz properties has focused on characteristic zero, we primarily consider the presence of the properties in positive characteristic. We study …