A calculus for the random generation of labelled combinatorial structures

Flajolet, Philippe; Zimmermann, Paul; Cutsem, Bernard Van

doi:10.1016/0304-3975(94)90226-7

Cited by 236 publications

(233 citation statements)

References 11 publications

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“…Analogous operators are admissible in the unlabelled case: disjoint unions ('+' or Union), Cartesian (or unlabelled) products ('×' or Prod), sequences (Seq), powersets (PSet), sets (Set) 2 , cycles (Cycle), substitutions ('•' or Subst) and sequences, powersets, sets and cycles with restricted cardinality. In Table 1 we summarize the relations between these constructions and the corresponding generating functions 3 (see also [10]). We briefly describe now the combinatorial operators mentioned above:…”

Section: Admissible Operatorsmentioning

confidence: 99%

Combinatorial structures to modeling simple games and applications

Molinero

2017

AIP Conference Proceedings

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Abstract. We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-)heuristics algorithms and parallel programming, among others.

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Section: Admissible Operatorsmentioning

confidence: 99%

Combinatorial structures to modeling simple games and applications

Molinero

2017

AIP Conference Proceedings

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“…Other algorithmic problems we do not consider here are: systematic generation of words (e.g., Dyck words), ranking, unranking, and random generation of words, see e.g., [Ru78], [BBG90] and [FZC94]. All of these are used in order to code combinatorial structures.…”

Section: To Algorithmicsmentioning

confidence: 99%

Combinatorics on Words – A Tutorial

Berstel¹,

Karhumäki²

2004

Current Trends in Theoretical Computer Science

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“…For instance, recursive methods [8] or Boltzmann samplers [7], which have been used for deterministic automata [6,2,9], rely on a good recursive description of the input, which is not known for acyclic automata. To our knowledge, the only combinatorial result on acyclic automata is due to Liskovets [11], who gave a close formula for the number of acyclic automata, but which cannot be directly translate into a good recursive description.…”

Section: Introductionmentioning

confidence: 99%