منابع مشابه
The pure descent statistic on permutations
We introduce a new statistic based on permutation descents which has a distribution given by the Stirling numbers of the first kind, i.e., with the same distribution as for the number of cycles in permutations. We study this statistic on the sets of permutations avoiding one pattern of length three by giving bivariate generating functions. As a consequence, new classes of permutations enumerate...
متن کاملThe Descent Statistic on 123-avoiding Permutations
We exploit Krattenthaler’s bijection between 123-avoiding permutations and Dyck paths to determine the Eulerian distribution over the set Sn(123) of 123-avoiding permutations in Sn. In particular, we show that the descents of a permutation correspond to valleys and triple ascents of the associated Dyck path. We get the Eulerian numbers of Sn(123) by studying the joint distribution of these two ...
متن کاملA Probabilistic Approach to the Descent Statistic
We present a probabilistic approach to studying the descent statistic based upon a two-variable probability density. This density is log concave and, in fact, satisfies a higher order concavity condition. From these properties we derive quadratic inequalities for the descent statistic. Using Fourier series, we give exact expressions for the Euler numbers and the alternating r-signed permutation...
متن کاملThe Cycle Descent Statistic on Permutations
In this paper we study the cycle descent statistic on permutations. Several involutions on permutations and derangements are constructed. Moreover, we construct a bijection between negative cycle descent permutations and Callan perfect matchings.
متن کاملThe descent statistic on involutions is not log -
We establish a combinatorial connection between the sequence (in,k) counting the involutions on n letters with k descents and the sequence (an,k) enumerating the semistandard Young tableaux on n cells with k symbols. This allows us to show that the sequences (in,k) are not log-concave for some values of n, hence answering a conjecture due to F. Brenti.
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 1998
ISSN: 0218-0006,0219-3094
DOI: 10.1007/bf01608482