Abstract
| Language | English |
|---|---|
| Pages | 123–134 |
| Number of pages | 12 |
| Journal | Pure Mathematics and Applications |
| Volume | 17 |
| Issue number | 1-2 |
| Publication status | Published - 2007 |
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Keywords
- compositions
- partially ordered generalized patterns
- non-over-lapping occurrences
- generating functions
Cite this
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Avoidance of partially ordered patterns in compositions. / Heubach, Silvia; Kitaev, Sergey; Mansour, Toufik.
In: Pure Mathematics and Applications, Vol. 17, No. 1-2, 2007, p. 123–134.Research output: Contribution to journal › Article
TY - JOUR
T1 - Avoidance of partially ordered patterns in compositions
AU - Heubach, Silvia
AU - Kitaev, Sergey
AU - Mansour, Toufik
PY - 2007
Y1 - 2007
N2 - A partially ordered (generalized) pattern (POP) is a generalized pattern some of whose letters are incomparable. In this paper, we study avoidance of POPs in compositions and generalize results for avoidance of POPs in permutations and words. Specifically, we obtain results for the generating functions for the number of compositions that avoid shuffle patterns and multi-patterns. In addition, we give the generating function for the distribution of the maximum number of non-overlapping occurrences of a segmented POP t among the compositions of n, provided we know the generating function for the number of compositions of n that avoid t.
AB - A partially ordered (generalized) pattern (POP) is a generalized pattern some of whose letters are incomparable. In this paper, we study avoidance of POPs in compositions and generalize results for avoidance of POPs in permutations and words. Specifically, we obtain results for the generating functions for the number of compositions that avoid shuffle patterns and multi-patterns. In addition, we give the generating function for the distribution of the maximum number of non-overlapping occurrences of a segmented POP t among the compositions of n, provided we know the generating function for the number of compositions of n that avoid t.
KW - compositions
KW - partially ordered generalized patterns
KW - non-over-lapping occurrences
KW - generating functions
UR - http://puma.dimai.unifi.it/17_1_2.php
UR - https://personal.cis.strath.ac.uk/sergey.kitaev/index_files/Papers/POPs-in-compositions.pdf
M3 - Article
VL - 17
SP - 123
EP - 134
JO - Pure Mathematics and Applications
T2 - Pure Mathematics and Applications
JF - Pure Mathematics and Applications
SN - 1218-4586
IS - 1-2
ER -