Minimal Overlapping Patterns in Colored Permutations.
ELECTRONIC JOURNAL OF COMBINATORICS(2011)
摘要
A pattern P of length j has the minimal overlapping property if two consecutive occurrences of the pattern can overlap in at most one place, namely, at the end of the first consecutive occurrence of the pattern and at the start of the second consecutive occurrence of the pattern. For patterns P which have the minimal overlapping property, we derive a general formula for the generating function for the number of consecutive occurrences of P in words, permutations and k-colored permutations in terms of the number of maximum packings of P which are patterns of minimal length which has n consecutive occurrences of the pattern P. Our results have as special cases several results which have appeared in the literature. Another consequence of our results is to prove a conjecture of Elizalde that two permutations alpha and beta of size j which have the minimal overlapping property are strongly c-Wilf equivalent if alpha and beta have the same first and last elements.
更多查看译文
关键词
patterns
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络