Add to ORKGFor a permutation π in the symmetric group Sn let the total degree be its valency in the Hasse diagram of the strong Bruhat order on Sn, and let the down degree be the number of permutations which are covered by π in the strong Bruhat order. The maxima of the total degree and the down degree and their values at a random permutation are computed. Proofs involve variants of a classical theorem of Turán from extremal graph theory
The descent set D(w) of a permutation w of 1, 2,..., n is a standard and wellstudied statistic. We i...
Abstract. This paper examines two major results concerning the symmetric group, Sn. The first result...
We define a partial order on the symmetric group S_n of degree n by x ≥ y iff y = a_1 ··· a_kx with ...
AbstractThe definitions of descent, excedance, major index, inversion index and Denert's statistics ...
This thesis describes a line of work, much of it joint with Yibo Gao, which began with our proof of ...
Define a partial order ≤B on the symmetric group Sn as follows: given pi, σ ∈ Sn, we say pi ≤B σ if ...
Abstract. We give explicit, asymptotically sharp bounds for the probability that a pair of random pe...
AbstractThe distribution of descents in a fixed conjugacy class ofSnis studied and it is shown that ...
The descent set D(w) of a permutation w of 1, 2,..., n is a standard and well-studied statistic. We ...
We give explicit, asymptotically sharp bounds for the probability that a pair of random permutations...
AbstractWe study asymptotics of an irreducible representation of the symmetric group Sn correspondin...
AbstractWe prove a conjecture of Erdös and Turán concerning the average order of the elements in the...
AbstractWe extend Stanley's work on alternating permutations with extremal number of fixed points in...
2018-04-06The distribution of descents in certain conjugacy classes of Sₙ have been previously studi...
The definitions of descent, excedance, major index, inversion index and Denert's statistic for ...
The descent set D(w) of a permutation w of 1, 2,..., n is a standard and wellstudied statistic. We i...
Abstract. This paper examines two major results concerning the symmetric group, Sn. The first result...
We define a partial order on the symmetric group S_n of degree n by x ≥ y iff y = a_1 ··· a_kx with ...
AbstractThe definitions of descent, excedance, major index, inversion index and Denert's statistics ...
This thesis describes a line of work, much of it joint with Yibo Gao, which began with our proof of ...
Define a partial order ≤B on the symmetric group Sn as follows: given pi, σ ∈ Sn, we say pi ≤B σ if ...
Abstract. We give explicit, asymptotically sharp bounds for the probability that a pair of random pe...
AbstractThe distribution of descents in a fixed conjugacy class ofSnis studied and it is shown that ...
The descent set D(w) of a permutation w of 1, 2,..., n is a standard and well-studied statistic. We ...
We give explicit, asymptotically sharp bounds for the probability that a pair of random permutations...
AbstractWe study asymptotics of an irreducible representation of the symmetric group Sn correspondin...
AbstractWe prove a conjecture of Erdös and Turán concerning the average order of the elements in the...
AbstractWe extend Stanley's work on alternating permutations with extremal number of fixed points in...
2018-04-06The distribution of descents in certain conjugacy classes of Sₙ have been previously studi...
The definitions of descent, excedance, major index, inversion index and Denert's statistic for ...
The descent set D(w) of a permutation w of 1, 2,..., n is a standard and wellstudied statistic. We i...
Abstract. This paper examines two major results concerning the symmetric group, Sn. The first result...
We define a partial order on the symmetric group S_n of degree n by x ≥ y iff y = a_1 ··· a_kx with ...