6533b7cffe1ef96bd1258569
RESEARCH PRODUCT
A permutation code preserving a double Eulerian bistatistic
Vincent VajnovszkiJean-luc Barilsubject
FOS: Computer and information sciencesPolynomialDiscrete Mathematics (cs.DM)0102 computer and information sciences01 natural sciencesBijective proofCombinatoricsSet (abstract data type)symbols.namesakeEquidistributed sequence[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]FOS: MathematicsDiscrete Mathematics and CombinatoricsMathematics - Combinatorics0101 mathematicsComputingMilieux_MISCELLANEOUSMathematicsConjectureMathematics::CombinatoricsApplied Mathematics010102 general mathematicsGenerating functionEulerian path010201 computation theory & mathematicssymbolsBijectionCombinatorics (math.CO)Computer Science - Discrete Mathematicsdescription
Visontai conjectured in 2013 that the joint distribution of ascent and distinct nonzero value numbers on the set of subexcedant sequences is the same as that of descent and inverse descent numbers on the set of permutations. This conjecture has been proved by Aas in 2014, and the generating function of the corresponding bistatistics is the double Eulerian polynomial. Among the techniques used by Aas are the M\"obius inversion formula and isomorphism of labeled rooted trees. In this paper we define a permutation code (that is, a bijection between permutations and subexcedant sequences) and show the more general result that two $5$-tuples of set-valued statistics on the set of permutations and on the set of subexcedant sequences, respectively, are equidistributed. In particular, these results give a bijective proof of Visontai's conjecture.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-06-25 |