Combinatorial Gray codes
Combinatorial Gray codes
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组合格雷码
DOI：
10.1137/0209013
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发表时间：
1980
期刊：
影响因子：
--
通讯作者：
S. Williamson
中科院分区：
文献类型：
--
作者：
J. Joichi;D. White;S. Williamson
我们认为family $ \ {{\ bf c}（n，k）：o \ leqq k \ leqq n \} $，其中每个$ {\ bf c}（\ bf c}（n，k）$是一组组合对象，$ c （n，k）= | {\ bf c}（n，k）| $满足递归$ c（n，k）= a_ {n，k} c（n -1，k -1） + b_ {n ，k} c（n-1，k）$，$ {\ bf c}（n，k）$中的每个对象均由我们研究“无循环”或“均匀边界的过渡”。算法，即在集合上产生线性订单$ {\ bf c}（n，k）$的算法，以便代表连续对象的向量“彼此接近”（组合灰色代码）。统一界限的操作，均匀边界的过渡算法，无环算法，二进制反射的灰色代码，组合灰色代码，二项式网格
We consider families $\{ {\bf C}(n,k):O \leqq k \leqq n\} $ where each ${\bf C}(n,k)$ is a set of combinatorial objects, $C(n,k) = |{\bf C}(n,k)|$ satisfies a recursion $C(n,k)= a_{n,k}C(n - 1,k - 1) + b_{n,k} C(n - 1,k)$, and each object in ${\bf C}(n,k)$ is represented by an n-vector. We study “loop-free” or “uniformly bounded transition” algorithms, i.e., algorithms which yield linear orders on the sets ${\bf C}(n,k)$ so that the vectors representing consecutive objects are “close to each other” (combinatorial Gray codes).Key words. listing algorithms, uniformly bounded operations, uniformly bounded transition algorithms, loop-free algorithms, binary reflected Gray codes, combinatorial Gray codes, binomial grids