S. Sundaram, The homology of partitions with an even number of blocks, J. Algebraic Combin. 4 (1995), 69#92.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Hence Propositions 8.1 and 8.2 can be translated into results about these classes of permutations and their descent sets. To avoid being lengthy, we refer the reader to the literature for the definitions of these permutation classes and their relation to the cd index: for simsun permutations, see [24, 27]; for Andre# permutations, see [21] for signed Andre# permutations, see [10, 21] and for signed simsun permutations, see [11] Proposition 8.3. The number of simsun permutations in S n 1 with descent set S and the number of Andre# permutations in S n 1 with descent set S is equal to 2 S n 1 ....

S. Sundaram, The homology of partitions with an even number of blocks, J. Algebraic Combin. 4 (1995), 69#92.

..... There is a relation between the cd index of the Boolean algebra B n and certain classes of permutations. For instance, the cd index of B n is a refined enumeration of Andre permutations [17] Similarly, it is also a refined enumeration of simsun permutations, first defined by Simion and Sundaram [22, 23]. Another known example of a poset permutations pair is the cubical lattice and signed Andre permutations [8, 17] This motivates us to ask the following question. Given an Eulerian poset P , is it possible to find a canonical class of permutations which correspond to the cd index of the poset P ....

....a new maximal element M and a minimal element m to the set S # 0 . Then the following identities hold: #(Pyr(P ) V ( Insert(T , M) M ) #(Prism(P ) V ( Insert(T , M) M ) Simion and Sundaram defined a class of permutations called simsun permutations; see [22, page 267] and [23]. We will now see how simsun permutations are closely related with the operations Insert(T , n) and T n on permutations. A simsun permutation # of length n is a augmented permutation # = 0, s 1 , s n ) on the set . n of length n such that for all 0 n if we remove the k ....

S. Sundaram, The Homology of Partitions with an Even Number of Blocks, J. Algebraic Combin. 4 (1995), 69-92.

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S. Sundaram, The homology of partitions with an even number of blocks, J. Algebraic Combinatorics 4 (1995), 69-92.

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S. Sundaram, The homology of partitions with an even number of blocks, J. Algebraic Combinatorics 4 (1995), 69--92.

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