On permutations which are 1324 and 2143 avoiding
نویسنده
چکیده
We consider permutations which are 1324 and 2143 avoiding, where 2143 avoiding means that it is 2143 avoiding with the additional Bruhat restriction {2 ↔ 3}. In particular, for every permutation π we will construct a linear map Lπ and a labeled graph Gπ and will show that the following three conditions are equivalent: π is 1324 and 2143 avoiding; Lπ is onto; Gπ is a forest. We will also give some properties of Gπ and show that the number of π ∈ Sn whose graph is a path is 2n−1 − 1.
منابع مشابه
Operations on posets and rational identities of type A
(xi − xj) . The patterns appear in geometry, characterizing some families of Schubert varieties. Schubert varieties are indexed by permutations, and the varieties which are non singular are those whose indexing permutation does not contain the pattern 2143 nor the pattern 1324. In [2], Cortez has described geometrical properties of Schubert varieties for permutations avoiding the patterns 1324 ...
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