A Bijection between Atomic Partitions and Unsplitable Partitions
نویسندگان
چکیده
منابع مشابه
A Bijection between Atomic Partitions and Unsplitable Partitions
In the study of the algebra NCSym of symmetric functions in noncommutative variables, Bergeron and Zabrocki found a free generating set consisting of power sum symmetric functions indexed by atomic partitions. On the other hand, Bergeron, Reutenauer, Rosas, and Zabrocki studied another free generating set of NCSym consisting of monomial symmetric functions indexed by unsplitable partitions. Can...
متن کاملA Bijection between Shuffles and Set Partitions
Recall from Garsia’s paper that Ba is the group algebra Q(Sn) element Ba = 1 2 3 · · · a Wa,n = ∑ α∈Sa α Wa,n, where Wa,n is the word Wa,n = (a+ 1)(a+ 2) · · ·n. The motivation is that we have a deck of cards labelled 1, 2, . . . , n, and Ba represents all possible decks that may result from removing the cards 1, 2, . . . , a and then inserting them back into the deck (consisting of the cards a...
متن کاملA bijection between certain non-crossing partitions and sequences
We present a bijection between non-crossing partitions of the set [2n+1] into n+1 blocks such that no block contains two consecutive integers, and the set of sequences {si}n1 such that 1 ≤ si ≤ i, and if si = j, then si−r ≤ j − r for 1 ≤ r ≤ j − 1.
متن کاملA bijection between dominant Shi regions and core partitions
It is well-known that Catalan numbers Cn = 1 n+1 ( 2n n ) count the number of dominant regions in the Shi arrangement of type A, and that they also count partitions which are both n-cores as well as (n + 1)-cores. These concepts have natural extensions, which we call here the m-Catalan numbers and m-Shi arrangement. In this paper, we construct a bijection between dominant regions of the m-Shi a...
متن کاملA bijection between (bounded) dominant Shi regions and core partitions
It is well-known that Catalan numbers Cn = 1 n+1 ( 2n n ) count the number of dominant regions in the Shi arrangement of type A, and that they also count partitions which are both n-cores as well as (n + 1)-cores. These concepts have natural extensions, which we call here the m-Catalan numbers and m-Shi arrangement. In this paper, we construct a bijection between dominant regions of the m-Shi a...
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: 2011
ISSN: 1077-8926
DOI: 10.37236/494