We construct an explicit generating sets Fn and F̃n of the alternating and the symmetric groups, which make the Cayley graphs C(Alt(n), Fn) and C(Sym(n), F̃n) a family of bounded degree expanders for all sufficiently large n. These expanders have many applications in the theory of random walks on groups and other areas of mathematics. A finite graph Γ is called an ǫ-expander for some ǫ ∈ (0, 1), ...

We introduce the notion of 321-avoiding permutations in the affine Weyl group W of type An−1 by considering the group as a George group (in the sense of Eriksson and Eriksson). This enables us to generalize a result of Billey, Jockusch and Stanley to show that the 321-avoiding permutations in W coincide with the set of fully commutative elements; in other words, any two reduced expressions for ...

We provide a short proof on the change-of-basis coefficients from Specht basis to Kazhdan-Lusztig basis, using theory for parabolic Hecke algebra.

We show that the Littlewood-Richardson coefficients are values at 1 of certain parabolic Kazhdan-Lusztig polynomials for affine symmetric groups. These q-analogues of Littlewood-Richardson multiplicities coincide with those previously introduced in [21] in terms of ribbon tableaux.

We show that the Littlewood-Richardson coeecients are values at 1 of certain parabolic Kazhdan-Lusztig polynomials for aane symmetric groups. These q-analogues of Littlewood-Richardson multiplicities coincide with those previously introduced in 21] in terms of ribbon tableaux.