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 BousquetM\'elou, Claesson, Dukes, and Kitaev in \cite{BCDK}, who showed that ascent sequences of length $n$ are in 1to1 correspondence with \tptfree posets of size $n$. In this paper, we introduce a generalization of ascent sequences, which we call {\em $p$ascent sequences}, where $p \geq 1$. A sequence $(a_1, \ldots, a_n)$ of nonnegative integers is a $p$ascent 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 \cite{KR} by enumerating $p$ascent sequences with respect to the number of $0$s. We also generalize a result of Dukes, Kitaev, Remmel, and Steingr\'{\i}msson in \cite{DKRS} by finding the generating function for the number of $p$ascent sequences which have no consecutive repeated elements. Finally, we initiate the study of patternavoiding $p$ascent 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:  22 Jun 2017 15:07 
URI:  http://strathprints.strath.ac.uk/id/eprint/56071 
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