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Probabilistic Partitive Partitioning (PPP)
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies can be achieved by reducing the input space if a minimal loss of information can be achieved.
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The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the algebra depend polynomially on a parameter.
Tom Halverson, Arun Ram
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Multiplicative Partitions [PDF]
New formulas for the multiplicative partition function are developed. Besides giving a fast algorithm for generating these partitions, new identities for additive partitions and the Riemann zeta function are also produced.
Marc Chamberland +3 more
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New results and conjectures on 2-partitions of multisets [PDF]
The interplay between integer sequences and partitions has led to numerous interesting results, with implications in generating functions, integral formulae, or combinatorics.
Andrica, D. +5 more
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Plane partitions in the work of Richard Stanley and his school [PDF]
These notes provide a survey of the theory of plane partitions, seen through the glasses of the work of Richard Stanley and his school.
C. Krattenthaler
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An extension of MacMahon's equidistribution theorem to ordered set partitions [PDF]
We prove a conjecture of Haglund which can be seen as an extension of the equidistribution of the inversion number and the major index over permutations to ordered set partitions.
J. Remmel, A. Wilson
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Reconstruction of Partitions [PDF]
For the partition $x=[x_1\ge x_2\ge \cdots\ge x_k]$ of the integer $n=\sum_{i}\, x_{i}$ a $t$-deletion is a partition $y=[y_1\ge y_2\ge \cdots\ge y_k]$ with $x_{i}\geq y_{i}\geq 0$ and $\sum_{i}\, (x_{i}-y_{i})=t$. We prove that all partitions of $n$ are reconstructible from their $t$–deletions if $n$ is sufficiently large in relation to $t$.
Pretzel, Oliver, Siemons, Johannes
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Methodology for automatic recovering of 3D partitions from unstitched faces of non-manifold CAD models [PDF]
Data exchanges between different software are currently used in industry to speed up the preparation of digital prototypes for Finite Element Analysis (FEA).
PERNOT, Jean-Philippe +1 more
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Bayesian nonparametric estimators derived from conditional Gibbs structures [PDF]
We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail.
PRUENSTER, IGOR +5 more
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