The first ascent of size $d$ or more in compositions
A composition of a positive integer $n$ is a finite sequence of positive integers $a_1, a_2, \ldots, a_k$ such that $a_1+a_2+ \cdots +a_k=n$. Let $d$ be a fixed nonnegative integer. We say that we have an ascent of size $d$ or more at position $i$, if $a_{i+1}\geq a_i+d$. We study the average positi...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2006-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3509/pdf |
| _version_ | 1827324135486783488 |
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| author | Charlotte Brennan Arnold Knopfmacher |
| author_facet | Charlotte Brennan Arnold Knopfmacher |
| author_sort | Charlotte Brennan |
| collection | DOAJ |
| description | A composition of a positive integer $n$ is a finite sequence of positive integers $a_1, a_2, \ldots, a_k$ such that $a_1+a_2+ \cdots +a_k=n$. Let $d$ be a fixed nonnegative integer. We say that we have an ascent of size $d$ or more at position $i$, if $a_{i+1}\geq a_i+d$. We study the average position, initial height and end height of the first ascent of size $d$ or more in compositions of $n$ as $n \to \infty$. |
| first_indexed | 2024-04-25T02:03:53Z |
| format | Article |
| id | doaj.art-538577127383427abcc6de6aef4e3d58 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:53Z |
| publishDate | 2006-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-538577127383427abcc6de6aef4e3d582024-03-07T14:34:36ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502006-01-01DMTCS Proceedings vol. AG,...Proceedings10.46298/dmtcs.35093509The first ascent of size $d$ or more in compositionsCharlotte Brennan0Arnold Knopfmacher1The John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg]The John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg]A composition of a positive integer $n$ is a finite sequence of positive integers $a_1, a_2, \ldots, a_k$ such that $a_1+a_2+ \cdots +a_k=n$. Let $d$ be a fixed nonnegative integer. We say that we have an ascent of size $d$ or more at position $i$, if $a_{i+1}\geq a_i+d$. We study the average position, initial height and end height of the first ascent of size $d$ or more in compositions of $n$ as $n \to \infty$.https://dmtcs.episciences.org/3509/pdfcompositionsascentsgenerating functions[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds][info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Charlotte Brennan Arnold Knopfmacher The first ascent of size $d$ or more in compositions Discrete Mathematics & Theoretical Computer Science compositions ascents generating functions [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| title | The first ascent of size $d$ or more in compositions |
| title_full | The first ascent of size $d$ or more in compositions |
| title_fullStr | The first ascent of size $d$ or more in compositions |
| title_full_unstemmed | The first ascent of size $d$ or more in compositions |
| title_short | The first ascent of size $d$ or more in compositions |
| title_sort | first ascent of size d or more in compositions |
| topic | compositions ascents generating functions [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/3509/pdf |
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