<p>Given a sequence of $n$ symbols drawn from an alphabet of size $m$, I wish to count the number of sequences that have no more than $k$ occurrences of any symbol.  What is known about the asymptotic behavior of such sequences?  i.e., are there any reasonable upper bounds in terms of the three parameters $n$, $m$ and $k$?  There must be a name for this, but all I can find is the more specific Stockhausen sequence, which has other restrictions.</p>

CC BY-SA 3.0
2011-10-09T08:52:14.763Z
A useful summary of the Stockhausen sequences: http://www.combinatorics.org/Volume_3/PDF/v3i1r7.pdf
Suresh Venkat
CC BY-SA 3.0
2011-10-09T11:13:52.363Z
To make it clear, Stockhausen sequences are a different notion from what is being asked.
Tsuyoshi Ito
<reference-request><co.combinatorics>
Ref Request: Asymptotics of frequency restricted sequences
Kev
# Ref Request: Asymptotics of frequency restricted sequences

(Asked by: username_0 on 2011-10-09)

Given a sequence of $n$ symbols drawn from an alphabet of size $m$, I wish to count the number of sequences that have no more than $k$ occurrences of any symbol. What is known about the asymptotic behavior of such sequences? i.e., are there any reasonable upper bounds in terms of the three parameters $n$, $m$ and $k$? There must be a name for this, but all I can find is the more specific Stockhausen sequence, which has other restrictions.

**Tags:** reference-request, co.combinatorics

> **Comments:**
> **username_1**: A useful summary of the Stockhausen sequences: http://www.combinatorics.org/Volume_3/PDF/v3i1r7.pdf  
> **username_2**: To make it clear, Stockhausen sequences are a different notion from what is being asked.  

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## 0 answers

