80,867 research outputs found
Critical Pebbling Numbers of Graphs
We define three new pebbling parameters of a connected graph , the -,
-, and -critical pebbling numbers. Together with the pebbling number, the
optimal pebbling number, the number of vertices and the diameter of the
graph, this yields 7 graph parameters. We determine the relationships between
these parameters. We investigate properties of the -critical pebbling
number, and distinguish between greedy graphs, thrifty graphs, and graphs for
which the -critical pebbling number is .Comment: 26 page
A geometric Schur functor
We give geometric descriptions of the category C_k(n,d) of rational
polynomial representations of GL_n over a field k of degree d for d less than
or equal to n, the Schur functor and Schur-Weyl duality. The descriptions and
proofs use a modular version of Springer theory and relationships between the
equivariant geometry of the affine Grassmannian and the nilpotent cone for the
general linear groups. Motivated by this description, we propose
generalizations for an arbitrary connected complex reductive group of the
category C_k(n,d) and the Schur functor.Comment: 15 pages, v2 - notation made consistent and assumptions on
coefficients clarified. Accepted for publication in Selecta Mat
Exponential Iterated Integrals and the Relative Solvable Completion of the Fundamental Group of a Manifold
We develop a class of integrals on a manifold M called exponential iterated
integrals, an extension of K. T. Chen's iterated integrals. It is shown that
the matrix entries of any upper triangular representation of the fundamental
group of M can be expressed via these new integrals. The ring of exponential
iterated integrals contains the coordinate rings for a class of universal
representations, called relative solvable completions, of the fundamental
group. We consider exponential iterated integrals in the particular case of
fibered knot complements, where the fundamental group always has a faithful
relative solvable completion.Comment: 30 pages. New version is revised throughout, and includes a stronger
result in section 7 and more extensive discussion of example
Direct Contact Among Galactic Civilizations by Relativistic Interstellar Spaceflight
Direct contact among galactic populations by relativistic interstellar spacefligh
- …