1,991 research outputs found
Reconstructing multisets over commutative groupoids and affine functions over nonassociative semirings
A reconstruction problem is formulated for multisets over commutative
groupoids. The cards of a multiset are obtained by replacing a pair of its
elements by their sum. Necessary and sufficient conditions for the
reconstructibility of multisets are determined. These results find an
application in a different kind of reconstruction problem for functions of
several arguments and identification minors: classes of linear or affine
functions over nonassociative semirings are shown to be weakly reconstructible.
Moreover, affine functions of sufficiently large arity over finite fields are
reconstructible.Comment: 18 pages. Int. J. Algebra Comput. (2014
Analyzing Boltzmann Samplers for Bose-Einstein Condensates with Dirichlet Generating Functions
Boltzmann sampling is commonly used to uniformly sample objects of a
particular size from large combinatorial sets. For this technique to be
effective, one needs to prove that (1) the sampling procedure is efficient and
(2) objects of the desired size are generated with sufficiently high
probability. We use this approach to give a provably efficient sampling
algorithm for a class of weighted integer partitions related to Bose-Einstein
condensation from statistical physics. Our sampling algorithm is a
probabilistic interpretation of the ordinary generating function for these
objects, derived from the symbolic method of analytic combinatorics. Using the
Khintchine-Meinardus probabilistic method to bound the rejection rate of our
Boltzmann sampler through singularity analysis of Dirichlet generating
functions, we offer an alternative approach to analyze Boltzmann samplers for
objects with multiplicative structure.Comment: 20 pages, 1 figur
A Generic Approach to Coalition Formation
We propose an abstract approach to coalition formation that focuses on simple
merge and split rules transforming partitions of a group of players. We
identify conditions under which every iteration of these rules yields a unique
partition. The main conceptual tool is a specific notion of a stable partition.
The results are parametrized by a preference relation between partitions of a
group of players and naturally apply to coalitional TU-games, hedonic games and
exchange economy games.Comment: 21 pages. To appear in International Game Theory Review (IGTR
Symmetric Group Character Degrees and Hook Numbers
In this article we prove the following result: that for any two natural
numbers k and j, and for all sufficiently large symmetric groups Sym(n), there
are k disjoint sets of j irreducible characters of Sym(n), such that each set
consists of characters with the same degree, and distinct sets have different
degrees. In particular, this resolves a conjecture most recently made by
Moret\'o. The methods employed here are based upon the duality between
irreducible characters of the symmetric groups and the partitions to which they
correspond. Consequently, the paper is combinatorial in nature.Comment: 24 pages, to appear in Proc. London Math. So
Meinardus' theorem on weighted partitions: extensions and a probabilistic proof
We give a probalistic proof of the famous Meinardus' asymptotic formula for
the number of weighted partitions with weakened one of the three Meinardus'
conditions, and extend the resulting version of the theorem to other two
classis types of decomposable combinatorial structures, which are called
assemblies and selections. The results obtained are based on combining
Meinardus' analytical approach with probabilistic method of Khitchine.Comment: The version contains a few minor corrections.It will be published in
Advances in Applied Mathematic
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