论文标题
避免模式和大惊
Pattern-avoidance and Fuss-Catalan numbers
论文作者
论文摘要
我们研究了一部分排列，其中条目仅限于与索引相同的剩余，modulo一些整数$ k \ geq 2 $。我们表明，当对排列施加经典的132-或213避免限制时，我们会恢复大惊小怪的 - 卡塔兰数字和一些raney数字的特殊情况。 出乎意料的是，当我们对加泰罗尼亚州次要功能的加泰罗尼亚家族施加mod $ k $限制时，也有类似的声明。 最后，我们完全列举了mod- $ k $偏置排列的所有组合，避免了两种长度3的模式。这与Simion和Schmidt的系统研究类似，避免了两种长度3的模式。
We study a subset of permutations, where entries are restricted to having the same remainder as the index, modulo some integer $k \geq 2$. We show that when also imposing the classical 132- or 213-avoidance restriction on the permutations, we recover the Fuss--Catalan numbers and some special cases of the Raney numbers. Surprisingly, an analogous statement also holds when we impose the mod $k$ restriction on a Catalan family of subexcedant functions. Finally, we completely enumerate all combinations of mod-$k$-alternating permutations, avoiding two patterns of length 3. This is analogous to the systematic study by Simion and Schmidt, of permutations avoiding two patterns of length 3.
