We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier’s verdict is a function of the XOR of the two bits received. Such… (More)

In this extended abstract, we give a complete description and enumeration of smooth and rationally smooth Schubert varieties in finite type. In particular, we show that rationally smooth Schubert… (More)

We show that an element w of a finite Weyl group W is rationally smooth if and only if the hyperplane arrangement I(w) associated to the inversion set of w is inductively free, and the product (d1… (More)

Parabolic subgroups WI of Coxeter systems (W,S), as well as their ordinary and double quotients W/WI and WI\W/WJ , appear in many contexts in combinatorics and Lie theory, including the geometry and… (More)

In the symmetric group on a set of size 2n, let P2n denote the conjugacy class of involutions with no fixed points (equivalently, we refer to these as “pairings”, since each disjoint cycle has length… (More)

We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier’s verdict is a function of the XOR of the two bits received. We… (More)

Given an element w of a Coxeter group, let ai(w) be the number of elements less than w in Bruhat order. A theorem of Björner and Ekedahl states that if W is crystallographic, then ai(w) ≤ aj(w) for… (More)

The hyperlinear profile of a group measures the growth rate of the dimension of unitary approximations to the group. We construct a finitely-presented group whose hyperlinear profile is at least… (More)