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Results tagged with gr.group-theory
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user 50509
Questions about the branch of algebra that deals with groups.
1
vote
0
answers
167
views
Are these sequences, associated to integer partitions, always log-concave?
Let $\mathrm{CO}(m)$ be the set of all compositions of the
positive integer $m$. By a composition of $m$, I mean a finite
sequence $(m_1,\ldots,m_k)$ of positive integers with sum $\sum
m_i=m$.
The …
- 481
2
votes
Accepted
Representation of $\mathrm{AGL}(V)$ on the homology of the poset of affine subspaces of $V$
I suspect that
Solomon, Louis The affine group. I. Bruhat decomposition.
proves what you are looking for.
Let $A_n(q)$ denote the poset of proper affine subspaces of $\mathbf{F}_q^n$. The only non-van …
- 481
4
votes
Applications of Frobenius theorem and conjecture
Here is an application of Frobenius theorem of $1907$. Let $G$ be a finite group and $p$ a prime number. Write $G_p$ for the set of elements of $G$ of $p$-power order and $|G|_p$ for the $p$-part of t …
- 481