77 research outputs found
Edwards Curves and Gaussian Hypergeometric Series
Let be an elliptic curve described by either an Edwards model or a
twisted Edwards model over , namely, is defined by one of the
following equations mod , or,
mod , respectively. We express the
number of rational points of over using the Gaussian
hypergeometric series where and are the trivial and
quadratic characters over respectively. This enables us to
evaluate for some elliptic curves , and prove the
existence of isogenies between and Legendre elliptic curves over
Tensor algebras and displacement structure. IV. Invariant kernels
In this paper we investigate the class of invariant positive definite kernels
on the free semigroup on N generators. We provide a combinatorial description
of the positivity of the kernel in terms of Dyck paths and then we find a
displacement equation that encodes the invariance property of the kernel.Comment: 19 pages, 5 figure
A combinatorial interpretation of the LDU-decomposition of totally positive matrices and their inverses
We study the combinatorial description of the LDU-decomposition of totally positive matrices. We give a description of the lower triangular L, the diagonal D, and the upper triangular U matrices of the LDU-decomposition of totally positive matrices in terms of the combinatorial structure of essential planar networks described by Fomin and Zelevinsky [5]. Similarly, we find a combinatorial description of the inverses of these matrices. In addition, we provide recursive formulae for computing the L, D, and U matrices of a totally positive matrix
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