The Cycle Descent Statistic on Permutations
نویسندگان
چکیده
منابع مشابه
The 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 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 کاملCounting Permutations with Given Cycle Structure and Descent Set
The purpose of this paper is to count permutations in S , with a given cycle structure and a given descent set. Our main result (Theorem 2.1) asserts that the number of these permutations can be expressed as a scalar product of two symmetric functions, one associated with the cycle structure and the other with the descent set. Both of these symmetric functions can be interpreted as characterist...
متن کاملCoherent Permutations with Descent Statistic andthe Boundary Problem for the Graph ofZigzag Diagrams
The graph of zigzag diagrams is a close relative of Young’s lattice. The boundary problem for this graph amounts to describing coherent random permutations with descent–set statistic, and is also related to certain positive characters on the algebra of quasisymmetric functions. We establish connections to some further relatives of Young’s lattice and solve the boundary problem by reducing it to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/5673