广义禁止模式

Generalized pattern avoidance

从对经典禁止模式的探讨出发,定义了广义禁止模式这个新概念,证明了广义有禁排列在代数运算Γ下的不变性.进一步讨论了广义禁止模式中的一类特殊模式——231模式,并对231广义有禁排列进行了分类和组合计算.最后,提出了一个猜想.关于广义禁止模式的讨论可为有禁排列问题的研究发展提供更加广阔的空间.

The notion of classical pattern avoidance is extended by defining a new kind of generalized pattern avoidance, and the invariance of generalized restricted permutations on the algebraic operation T is proved. Furthermore, one kind of the generalized pattern avoidance, that is, the pattern 231 is discussed. The classifications and combinatorial calculations for generalized 231 restricted permutations are given. At last, a conjecture is presented. The new generalized patterns avoidance may promote the research on restricted permutations.