Now showing items 1-6 of 6

• Cataland: Why the Fuß? ﻿

[OWP-2019-01] (Mathematisches Forschungsinstitut Oberwolfach, 2019-01-21)
The three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of these have known Fuß-Catalan generalizations. ...
• Congruences Associated with Families of Nilpotent Subgroups and a Theorem of Hirsch ﻿

[OWP-2019-16] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-27)
Our main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number ...
• Experimenting with Symplectic Hypergeometric Monodromy Groups ﻿

[OWP-2019-15] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-22)
We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results ...
• Group-Graded Rings Satisfying the Strong Rank Condition ﻿

[OWP-2019-22] (Mathematisches Forschungsinstitut Oberwolfach, 2019-08-16)
A ring $R$ satisfies the $\textit{strong rank condition}$ (SRC) if, for every natural number $n$, the free $R$-submodules of $R^n$ all have rank $\leq n$. Let $G$ be a group and $R$ a ring strongly graded by $G$ such that ...
• On a Group Functor Describing Invariants of Algebraic Surfaces ﻿

[OWP-2019-08] (Mathematisches Forschungsinstitut Oberwolfach, 2019-03-01)
Liedtke (2008) has introduced group functors $K$ and $\tilde K$, which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these functors are connected to the theory of ...
• On Residuals of Finite Groups ﻿

[OWP-2019-17] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-28)
A theorem of Dolfi, Herzog, Kaplan, and Lev [DHKL07, Thm. C] asserts that in a finite group with trivial Fitting subgroup, the size of the soluble residual of the group is bounded from below by a certain power of the group ...