TY - JOUR

T1 - Counting Stirling permutations by number of pushes

AU - Mansour, Toufik

AU - Shattuck, Mark

PY - 2020

Y1 - 2020

N2 - Let 풯(k)n denote the set of k-Stirling permutations having n distinct letters. Here, we consider the number of steps required (i.e., pushes) to rearrange the letters of a member of 풯(k)n so that they occur in non-decreasing order. We find recurrences for the joint distribution on 풯(k)n for the statistics recording the number of levels (i.e., occurrences of equal adjacent letters) and pushes. When k = 2, an explicit formula for the ordinary generating function of this distribution is also found. In order to do so, we determine the LU-decomposition of a certain infinite matrix having polynomial entries which enables one to compute explicitly the inverse matrix.

AB - Let 풯(k)n denote the set of k-Stirling permutations having n distinct letters. Here, we consider the number of steps required (i.e., pushes) to rearrange the letters of a member of 풯(k)n so that they occur in non-decreasing order. We find recurrences for the joint distribution on 풯(k)n for the statistics recording the number of levels (i.e., occurrences of equal adjacent letters) and pushes. When k = 2, an explicit formula for the ordinary generating function of this distribution is also found. In order to do so, we determine the LU-decomposition of a certain infinite matrix having polynomial entries which enables one to compute explicitly the inverse matrix.

U2 - https://doi.org/10.1515/puma-2015-0038

DO - https://doi.org/10.1515/puma-2015-0038

M3 - مقالة

SN - 1218-4586

VL - 29

SP - 17

EP - 27

JO - Pure Mathematics and Applications

JF - Pure Mathematics and Applications

IS - 1

ER -