论文标题
多重组合的组合
Combinatorics of Multicompositions
论文作者
论文摘要
安德鲁斯（Andrews）在2007年引入了带有某些有色零件的整数组成，以解决许多理论问题。整数组成允许零作为某些零件在2019年引入某些零件。我们在这两种组合物变种之间进行了两者的培训，并确定这些多组分的各种组合特性。特别是，我们按所有零件的数量，正零件数量和零数数量确定了多组分的计数。然后，从三种类型的组合物中工作，该组合物由斐波那契序列计数，我们发现计算具有类似限制的多重组件的序列。使用这些工具，我们为jacobsthal和pell序列的概括提供了求和公式的组合证明。
Integer compositions with certain colored parts were introduced by Andrews in 2007 to address a number-theoretic problem. Integer compositions allowing zero as some parts were introduced by Ouvry and Polychronakos in 2019. We give a bijection between these two varieties of compositions and determine various combinatorial properties of these multicompositions. In particular, we determine the count of multicompositions by number of all parts, number of positive parts, and number of zeros. Then, working from three types of compositions with restricted parts that are counted by the Fibonacci sequence, we find the sequences counting multicompositions with analogous restrictions. With these tools, we give combinatorial proofs of summation formulas for generalizations of the Jacobsthal and Pell sequences.
