A note on pAscent Sequences
Kitaev, Sergey and Remmel, Jeffrey (2017) A note on pAscent Sequences. Journal of Combinatorics, 8 (3). pp. 487506. ISSN 21563527

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Abstract
Ascent sequences were introduced by BousquetMélou, Claesson, Dukes, and Kitaev in [1], who showed that ascent sequences of length n are in 1to1 correspondence with (2+2)free posets of size n. In this paper, we introduce a generalization of ascent sequences, which we call pascent sequences, where p \geq 1. A sequence $(a_1, \ldots, a_n)$ of nonnegative integers is a pascent sequence if $a_0 =0$ and for all $i \geq 2$, $a_i$ is at most p plus the number of ascents in $(a_1, \ldots, a_{i1})$. Thus, in our terminology, ascent sequences are 1ascent sequences. We generalize a result of the authors in [9] by enumerating pascent sequences with respect to the number of 0s. We also generalize a result of Dukes, Kitaev, Remmel, and Steingrímsson in [4] by finding the generating function for the number of pascent sequences which have no consecutive repeated elements. Finally, we initiate the study of patternavoiding pascent sequences.
Item type:  Article 

ID code:  56071 
Keywords:  ascent sequences, pascent sequences, Electronic computers. Computer science, Computer Science(all) 
Subjects:  Science > Mathematics > Electronic computers. Computer science 
Department:  Faculty of Science > Computer and Information Sciences 
Depositing user:  Pure Administrator 
Date deposited:  05 Apr 2016 07:11 
Last modified:  25 Sep 2017 18:27 
URI:  https://strathprints.strath.ac.uk/id/eprint/56071 
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