On the n × n × n Rubik's Cube

Derangements on the n-cube

Chen, W.Y.C. and R.P. Stanley, Derangements on the n-cube, Discrete Mathematics 115 (1993) 65-15. Let Q. be the n-dimensional cube represented by a graph whose vertices are sequences of O’s and l’s of length n, where two vertices are adjacent if and only if they differ only at one position. A k-dimensional subcube or a k-face of Q. is a subgraph of Q. spanned by all the vertices u1 u2 u, with c...

On the Rational Recursive Sequence X_{N+1}=ƔX_{N-K}+(AX_N+BX_{N-K})⁄(CX_N-DX_{N-K})

Stratiied Random Walks on the N-cube

In this paper we present a method for analyzing a general class of ramdom walks on the n cube and certain subgraphs of it These walks all have the property that the transition probabilities depend only on the level of the point the walk is at For these walks we derive sharp bounds on their mixing rates i e the number of steps required to guarantee that the resulting distribution is close to the...

Stratified random walks on the n-cube

In this paper we present a method for analyzing a general class of random Ž . walks on the n-cube and certain subgraphs of it . These walks all have the property that the transition probabilities depend only on the level of the point at which the walk is. For these walks, we derive sharp bounds on their mixing rates, i.e., the number of steps required to Ž . guarantee that the resulting distrib...

Stratiied Random Walks on the N-cube

In this paper we present a method for analyzing a general class of ramdom walks on the n-cube (and certain subgraphs of it). These walks all have the property that the transition probabilities depend only on the level of the point the walk is at. For these walks, we derive sharp bounds on their mixing rates, i.e., the number of steps required to guarantee that the resulting distribution is clos...