Search results for "Bijections"

showing 2 items of 2 documents

Mahonian STAT on words

2016

In 2000, Babson and Steingrimsson introduced the notion of what is now known as a permutation vincular pattern, and based on it they re-defined known Mahonian statistics and introduced new ones, proving or conjecturing their Mahonity. These conjectures were proved by Foata and Zeilberger in 2001, and by Foata and Randrianarivony in 2006.In 2010, Burstein refined some of these results by giving a bijection between permutations with a fixed value for the major index and those with the same value for STAT , where STAT is one of the statistics defined and proved to be Mahonian in the 2000 Babson and Steingrimsson's paper. Several other statistics are preserved as well by Burstein's bijection.At…

FOS: Computer and information sciencesQA75[ INFO ] Computer Science [cs]Discrete Mathematics (cs.DM)Major index0102 computer and information sciencesMathematical Analysis01 natural sciencesWords and PermutationsCombinatorial problemsEquidistributionTheoretical Computer ScienceCombinatoricssymbols.namesakePermutationBijectionsFOS: MathematicsMathematics - CombinatoricsMathematical proofs[INFO]Computer Science [cs]0101 mathematicsStatisticMathematicsStatisticZ665Algebraic combinatoricsMathematics::CombinatoricsFormal power seriesPatternPermutationsEulerian path16. Peace & justiceComputer Science Applications010101 applied mathematics010201 computation theory & mathematicsCombinatoricsSignal ProcessingsymbolsBijectionCombinatorics (math.CO)Information SystemsComputer Science - Discrete Mathematics
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Statistics-preserving bijections between classical and cyclic permutations

2012

Recently, Elizalde (2011) [2] has presented a bijection between the set C"n"+"1 of cyclic permutations on {1,2,...,n+1} and the set of permutations on {1,2,...,n} that preserves the descent set of the first n entries and the set of weak excedances. In this paper, we construct a bijection from C"n"+"1 to S"n that preserves the weak excedance set and that transfers quasi-fixed points into fixed points and left-to-right maxima into themselves. This induces a bijection from the set D"n of derangements to the set C"n"+"1^q of cycles without quasi-fixed points that preserves the weak excedance set. Moreover, we exhibit a kind of discrete continuity between C"n"+"1 and S"n that preserves at each s…

0102 computer and information sciencesFixed point[ MATH.MATH-CO ] Mathematics [math]/Combinatorics [math.CO]01 natural sciencesCombinatorial problemsTheoretical Computer ScienceCyclic permutationSet (abstract data type)CombinatoricsBijections[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]0101 mathematicsComputingMilieux_MISCELLANEOUSMathematicsDescent (mathematics)Discrete mathematicsStatistics on permutationsMathematics::Combinatorics010102 general mathematicsDescentComputer Science ApplicationsDerangement010201 computation theory & mathematicsExcedenceSignal ProcessingBijectionBijection injection and surjectionMaximaInformation Systems
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