31 citations · 158 across the 54 of their papers we have counts for
7 papers · 1 filter
Increasing and Decreasing Subsequences of Permutations and Their Variants
Richard P. Stanley
We survey the theory of increasing and decreasing subsequences of permutations. Enumeration problems in this area are closely related to the RSK algorithm. The asymptotic behavior…
Longest alternating subsequences of permutations
Richard P. Stanley
The length is(w) of the longest increasing subsequence of a permutation w in the symmetric group S_n has been the object of much investigation. We develop comparable results for th…
An analogue of Young's lattice for compositions
Anders Bjorner, Richard Stanley
This paper has been withdrawn by the authors since it was discovered that most of its content was already known.
The Descent Set and Connectivity Set of a Permutation
Richard P. Stanley
The descent set D(w) of a permutation w of 1,2,...,n is a standard and well-studied statistic. We introduce a new statistic, the connectivity set C(w), and show that it is a kind o…
Chains in the Bruhat order
Alexander Postnikov, Richard P. Stanley
We study a family of polynomials whose values express degrees of Schubert varieties in the generalized complex flag manifold G/B. The polynomials are given by weighted sums over sa…
Ordering Events in Minkowski Space
Richard P. Stanley
We are given k points (events) in (n+1)-dimensional Minkowski space. Using the theory of hyperplane arrangments and chromatic polynomials, we obtain information the number of diffe…