9 D ec 1 99 7 Cycle Indices for the Finite Classical

9 D ec 1 99 7 Cycle Indices for the Finite Classical Groups By Jason

The Polya cycle index has been a key tool in understanding what a typical permutation π ∈ Sn ”looks like”. It is useful for studying properties of a permutation which depend only on its cycle structure. Here are some examples of theorems which can be proved using the cycle index. Lloyd and Shepp [25] showed that for any i < ∞, the joint distribution of (a1(π), · · · , ai(π)) for π chosen unifor...

1 5 D ec 1 99 9 FINITE POSETS AND FERRERS SHAPES

ua nt - p h / 99 12 11 5 v 1 2 8 D ec 1 99 9 The δ - deformation of the Fock space

A deformation of the Fock space based on the finite difference replacement for the derivative is introduced. The deformation parameter is related to the dimension of the finite analogue of the Fock space.

D ec 1 99 5 An Explicit Formula for the Number of Solutions of X 2 = 0 in Triangular Matrices Over a Finite Field

X iv :m at h/ 95 12 22 4v 1 [ m at h. C O ] 1 9 D ec 1 99 5 An Explicit Formula for the Number of Solutions of X = 0 in Triangular Matrices Over a Finite Field Shalosh B. EKHAD and Doron ZEILBERGER Abstract: We prove an explicit formula for the number of n × n upper triangular matrices, over GF (q), whose square is the zero matrix. This formula was recently conjectured by Sasha Kirillov and Ann...

ar X iv : m at h / 99 07 08 5 v 2 [ m at h . G R ] 1 7 D ec 1 99 9 LOOPS AND SEMIDIRECT PRODUCTS