کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6416497 | 1336829 | 2013 | 9 صفحه PDF | دانلود رایگان |
Suppose that the elements within each block of a partition Ï of [n]={1,2,â¦,n} are written in ascending order. By a parity succession, we will mean a pair of adjacent elements x and y within some block of Ï such that xâ¡y(mod2). Here, we consider the problem of counting the partitions of [n] according to the number of successions, extending recent results concerning successions on subsets and permutations. Using linear algebra, we determine a formula for the generating function which counts partitions having a fixed number of blocks according to size and number of successions. Furthermore, a special case of our formula yields an explicit recurrence for the generating function which counts the parity-alternating partitions of [n], i.e., those that contain no successions.
Journal: Linear Algebra and its Applications - Volume 439, Issue 9, 1 November 2013, Pages 2642-2650