stirling2

Denote the number of ways to partition a set of n objects into k non-empty subsets

Numbers

second

Stirling

kind

Compute the median ranking according to the Kemeny's axiomatic approach.
Rankings can or cannot contain ties, rankings can be both complete or incomplete.
The package contains both branch-and-bound algorithms and heuristic solutions recently proposed.
The searching space of the solution can either be restricted to the universe of the permutations or unrestricted to all possible ties.
The package also provide some useful utilities for deal with preference rankings, including both element-weight Kemeny distance and correlation coefficient.
This release declare as deprecated some functions that are still in the package for compatibility. Next release will not contains these functions.
Please type '?ConsRank-deprecated'
Essential references:
Emond, E.J., and Mason, D.W. (2002) <doi:10.1002/mcda.313>;
D'Ambrosio, A., Amodio, S., and Iorio, C. (2015) <doi:10.1285/i20705948v8n2p198>;
Amodio, S., D'Ambrosio, A., and Siciliano R. (2016) <doi:10.1016/j.ejor.2015.08.048>;
D'Ambrosio, A., Mazzeo, G., Iorio, C., and Siciliano, R. (2017) <doi:10.1016/j.cor.2017.01.017>;
Albano, A., and Plaia, A. (2021) <doi:10.1285/i20705948v14n1p117>.

Antonio DAmbrosio

ConsRank

Compute the Median Ranking(s) According to the Kemeny's
Axiomatic Approach

Antonio D'Ambrosio

Sonia Amodio

Giulio Mazzeo

Alessandro Albano

Antonella Plaia

stirling2 function

<dl><dt>n</dt>
<dd>(integer): the number of the objects</dd>
<dt>k</dt>
<dd>(integer &lt;=n): the number of the non-empty subsets (buckets)</dd></dl>

Arguments

Antonio D'Ambrosio <a href="/link/antdambr%40unina.it?package=ConsRank&version=2.1.5" data-mini-rdoc="ConsRank::antdambr@unina.it">antdambr@unina.it</a>

Author

Stirling numbers of the second kind — stirling2

<dl>

<dt>n</dt>
<dd>(integer): the number of the objects</dd>


<dt>k</dt>
<dd>(integer &lt;=n): the number of the non-empty subsets (buckets)</dd>

</dl>

Antonio D'Ambrosio <a href='mailto:antdambr@unina.it'>antdambr@unina.it</a>

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stirling2: Stirling numbers of the second kind

Description

Usage

Value

Arguments

Author

References

Examples

S		the stirling number of the second kind
SM		a matrix showing, for each k (on the columns) in how many ways the n objects (on the rows) can be partitioned