query: k-cycles and permutations
positive_passages.docid: 151805
positive_passages.text: Prove that $\tau (x_1 x_2 ... x_k) \tau^{-1} = (\tau(x_1) \tau(x_2) ... \tau (x_k))$
negative_passages.docid: 68638
negative_passages.text: Show that if $n\geq 3$, the complete graph on $n$ vertices $K_n$ contains a Hamiltonian cycle.
negative_passages.docid: 66842
negative_passages.text: Number of $n^2\times n^2$ permutation matrices with a 1 in each $n\times n$ subgrid
negative_passages.docid: 75227
negative_passages.text: If $S=\{1,2,\dots,n\}$ and $P_n(k)$ be the number of permutations of $S$ having $k$ fixed points, then $\sum_{k=0}^nk.P_{n}(k)=n!$
negative_passages.docid: 113015
negative_passages.text: Eulerian Paths in a Complete Graph $K_5$
negative_passages.docid: 108417
negative_passages.text: Cycles of length k in a complete simple graph with n vertices
negative_passages.docid: 155372
negative_passages.text: Find the number of permutations in $S_n$ containing fixed elements in one cycle
negative_passages.docid: 140199
negative_passages.text: Proof that disjoint cycles commute
negative_passages.docid: 41294
negative_passages.text: Permutation module of $S_n$
negative_passages.docid: 117862
negative_passages.text: Number of partitions of an $n$-element set into $k$ classes
negative_passages.docid: 85023
negative_passages.text: Permutation of n objects with restriction of adjacent pairs
negative_passages.docid: 110167
negative_passages.text: A conjecture with connection to the $abc$-conjecture
negative_passages.docid: 90256
negative_passages.text: Example of a simple graph isomorphic to a permutation group.
negative_passages.docid: 133270
negative_passages.text: Prove that the chromatic polynomial of a cycle graph $C_{n}$ equals $(k-1)^{n} + (k-1)(-1)^{n}$
negative_passages.docid: 137931
negative_passages.text: Problem from "The Theory of Finite Groups" by Kurzweil and Stellmacher
negative_passages.docid: 97314
negative_passages.text: Counting nearly-sorted permutations
negative_passages.docid: 26343
negative_passages.text: Number of certain (0,1)-matrices, Stanley's Enumerative Combinatorics