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Let $G$ be a finite group, $L(G)$ its subgroup lattice and $\mu$ the Möbius function. Consider the Euler totient of $G$ defined as follows: $$ \varphi(G) = \sum_{H \le G}\mu(H,G) |H| $$ Let $X=\{M_1, \...

How does one enumerate the distinct orbit classes of independent sets of the hypercube modulo symmetries of the hypercubes? The counting of the number of independent sets in an $n$-dimensional ...

Let $p$ be a prime number and $G=GL_n ( \mathbb{Z} / p \mathbb{Z} )$. Consider the set $U$ of upper-triangular matrices of $G$ having entries of $1$ on the diagonal. The cardinality of $U$ is $p^{\...

Let $L$ be a finite lattice with minimum $\hat{0}$ and maximum $\hat{1}$. The Möbius function $\mu$ for $L$ is defined recursively by: for $\forall a,b \in L$ with $a<b$, $\mu(b,b) = 1$ and $\mu(...