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HEIGHT FORMULAS FOR HOMOGENEOUS VARIETIES
HOMOGENEOUS VARIETIES Differential and integral calculus
2015/12/17
We use classicalSchubert calculus to evaluate the integral formula
of Kaiser and Kohler [KK] for the Faltings height of certain homogeneous
varieties in terms of combinatorial data, and verify thei...
Facet evolution on supported nanostructures:Effect of finite height
Facet evolution nanostructures finite height
2015/10/16
The surface of a nanostructure relaxing on a substrate consists of a finite number of interacting steps and often involves the expansion of facets. Prior theoretical studies of facet evolution have fo...
On the height of cyclotomic polynomials
cyclotomic polynomial inverse cyclotomic polynomial
2011/2/22
Let An denote the height of cyclotomic polynomial Φn,where n is a product of k distinct odd primes. We prove that An "k'(n)k−12k−1 −1 with −log "k c2k, c > 0. The same state...
Sub-Gaussian tail bounds for the width and height of conditioned Galton--Watson trees
Sub-Gaussian tail conditioned Galton--Watson trees
2010/11/23
We study the height and width of a Galton--Watson tree with offspring distribution B satisfying E(B)=1, 0 < Var(B) < infinity, conditioned on having exactly n nodes. Under this conditioning, we deriv...
Some conjectures on the maximal height of divisors of $x^n-1$
cyclotomic polynomials heights of polynomials
2010/12/14
Define B(n) to be the largest height of a polynomial in Z[x] dividing xn−1. We formulate a number of conjectures related to the value of B(n) when n is of a prescribed form. Additionally,we prov...
The distribution of height and diameter in random non-plane binary trees
distribution of height diameter in random non-plane binary trees
2010/12/1
This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees (“Otter trees”), when trees of a given size are taken with equal likelihood. The height of...