Zobrazeno 1 - 10
of 146 700
pro vyhledávání: '"derangements"'
Autor:
Burness, Timothy C., Fusari, Marco
Let $G \leqslant {\rm Sym}(\Omega)$ be a finite transitive permutation group and recall that an element in $G$ is a derangement if it has no fixed points on $\Omega$. Let $\Delta(G)$ be the set of derangements in $G$ and define $\delta(G) = |\Delta(G
Externí odkaz:
http://arxiv.org/abs/2409.01043
A sum rule for $r$-derangements obtained from the Cauchy product of exponential generating functions
Autor:
Pain, Jean-Christophe
We propose a sum rule for $r$-derangements (meaning that the elements are restricted to be in distinct cycles in the cycle decomposition) involving binomial coefficients. The identity, obtained using the Cauchy product of two exponential generating f
Externí odkaz:
http://arxiv.org/abs/2408.15927
Autor:
Garzoni, Daniele
We prove that if $G$ is a transitive permutation group of sufficiently large degree $n$, then either $G$ is primitive and Frobenius, or the proportion of derangements in $G$ is larger than $1/(2n^{1/2})$. This is sharp, generalizes substantially boun
Externí odkaz:
http://arxiv.org/abs/2409.03305
Autor:
Ellis, David, Harper, Scott
Let $G$ be a nontrivial finite permutation group of degree $n$. If $G$ is transitive, then a theorem of Jordan states that $G$ has a derangement. Equivalently, a finite group is never the union of conjugates of a proper subgroup. If $G$ is intransiti
Externí odkaz:
http://arxiv.org/abs/2408.16064
Autor:
Barbieri, Marco, Spiga, Pablo
Publikováno v:
Discrete Mathematics: 347(7): 114032 (2024)
We find a lower bound on the proportion of derangements in a finite transitive group that depends on the minimal nontrivial subdegree. As a consequence, we prove that, if $\Gamma$ is a $G$-vertex-transitive digraph of valency $d\ge 1$, then the propo
Externí odkaz:
http://arxiv.org/abs/2402.05089
Autor:
Ji, Kathy Q., Zhang, Dax T. X.
Publikováno v:
Europ. J. Combin. 124 (2025) 104083
The polynomial of the major index ${\rm maj}_W (\sigma)$ over the subset $T$ of the Coxeter group $W$ is called the Mahonian polynomial over $T$, where ${\rm maj}_W (\sigma)$ is a Mahonian statistic of an element $\sigma \in T$, whereas the polynomia
Externí odkaz:
http://arxiv.org/abs/2402.03644