80 research outputs found
Shape Avoiding Permutations
Permutations avoiding all patterns of a given shape (in the sense of
Robinson-Schensted-Knuth) are considered. We show that the shapes of all such
permutations are contained in a suitable thick hook, and deduce an exponential
growth rate for their number.Comment: 16 pages; final form, to appear in J. Combin. Theory, Series
The number of inversions of permutations with fixed shape
The Robinson-Schensted correspondence can be viewed as a map from
permutations to partitions. In this work, we study the number of inversions of
permutations corresponding to a fixed partition under this map.
Hohlweg characterized permutations having shape with the minimum
number of inversions. Here, we give the first results in this direction for
higher numbers of inversions. We give explicit conjectures for both the
structure and the number of permutations associated to where the
extra number of inversions is less than the length of the smallest column of
. We prove the result when has two columns.Comment: 19 pages, 2 figure
Two-sided cells in type (asymptotic case)
We compute two-sided cells of Weyl groups of type for the "asymptotic"
choice of parameters. We also obtain some partial results concerning
Kazhdan-Lusztig conjectures in this particular case.Comment: 20 pages, some misprints have been cleaned up in this second versio
The exotic Robinson-Schensted correspondence
We study the action of the symplectic group on pairs of a vector and a flag.
Considering the irreducible components of the conormal variety, we obtain an
exotic analogue of the Robinson-Schensted correspondence. Conjecturally, the
resulting cells are related to exotic character sheaves.Comment: 14 page
- …