24 citations · 67 across the 18 of their papers we have counts for
12 papers · 1 filter
Correlation functions for random involutions
Peter J. Forrester, Taro Nagao, Eric M. Rains
Our interest is in the scaled joint distribution associated with -increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifyi…
BC_n-symmetric abelian functions
Eric M. Rains
We construct a family of BC_n-symmetric biorthogonal abelian functions generalizing Koornwinder's orthogonal polynomials, and prove a number of their properties, most notably analo…
A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces
A. R. Calderbank, R. H. Hardin, E. M. Rains +2
By using totally isotropic subspaces in an orthogonal space Omega^{+}(2i,2), several infinite families of packings of 2^k-dimensional subspaces of real 2^i-dimensional space are co…
The Shadow Theory of Modular and Unimodular Lattices
E. M. Rains, N. J. A. Sloane
It is shown that an n-dimensional unimodular lattice has minimal norm at most 2[n/24] +2, unless n = 23 when the bound must be increased by 1. This result was previously known only…
On the Existence of Similar Sublattices
J. H. Conway, E. M. Rains, N. J. A. Sloane
Partial answers are given to two questions. When does a lattice Lambda contain a sublattice Lambda' of index N that is geometrically similar to Lambda? When is the sublattice "clea…
On Cayley's Enumeration of Alkanes (or 4-Valent Trees)
E. M. Rains, N. J. A. Sloane
Cayley's 1875 enumerations of centered and bicentered alkanes (unlabeled trees of valency at most 4) are corrected and extended -- possibly for the first time in 124 years.