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Counting good truth assignments of random k-SAT formulae
Random k-SAT Correlation Decay Uniqueness Gibbs Distribution
2015/8/21
We present a deterministic approximation algorithm to compute logarithm of the number of ‘good’ truth assignments for a random k-satisfiability (k-SAT) formula in polynomial time (by ‘good’ we m...
Wald Lecture I: Counting Bits with Kolmogorov and Shannon
Rate-Distortion Gaussian Process Entrop Ellipsoids
2015/8/21
Shannon’s Rate-Distortion Theory describes the number of bits needed to approximately
represent typical realizations of a stochastic process X = (X(t) : t ∈ T),while Kolmogorov’s
-entropy describes...
COUNTING THE FACES OF RANDOMLY-PROJECTED HYPERCUBES AND ORTHANTS, WITH APPLICATIONS
RANDOMLY-PROJECTED ORTHANTS
2015/8/21
Let RN
+ denote the positive orthant; the expected number of k-faces of
the random cone ARN
+ obeys Efk(ARN
+)/fk(RN
+) = 1 − PN−n,N−k. The
formula applies to numerous matrix e...
COUNTING FACES OF RANDOMLY-PROJECTED POLYTOPES WHEN THE PROJECTION RADICALLY LOWERS DIMENSION
RANDOMLY-PROJECTED RADICALLY LOWERS DIMENSION
2015/8/21
The modern trend in statistics and probability is to consider the case where both
the number of dimensions d and the sample size n are large [19, 21]. In that case, the
intuition fostered by the cla...
Caporaso and Harris derive recursive formulas counting nodal plane
curves of degree d and geometric genus g in the plane (through the appropriate number of xed
general points). We rephrase their ar...
Counting the World's Poor: Problems and Possible Solutions
Counting the World's Poor Problems Possible Solutions
2014/3/24
Counting the World's Poor: Problems and Possible Solutions。
An improved upper bound for the error in the zero-counting formulae for Dirichlet $L$-functions and Dedekind zeta-functions
the zero-counting formulae Dirichlet $L$-functions Dedekind zeta-functions Number Theory
2012/6/30
This paper contains new explicit upper bounds for the number of zeroes of Dirichlet L-functions and Dedekind zeta-functions in rectangles.
The set of Dyck paths of length $2n$ inherits a lattice structure from a bijection with the set of noncrossing partitions with the usual partial order. In this paper, we study the joint distribution o...
We present a new approach for counting trees, and we apply it to count multitype Cayley trees and to prove the multivariate Lagrange inversion formula. The gist of our approach is to exploit the symme...
Counting independent sets of a fixed size in graphs with a given minimum degree
graphs given minimum degree independent sets Combinatorics
2012/4/16
Galvin showed that for all fixed $\delta$ and sufficiently large $n$, the $n$-vertex graph with minimum degree $\delta$ that admits the most independent sets is the complete bipartite graph $K_{\delta...
Counting rational points over number fields on a singular cubic surface
rational points over number fields singular cubic surface Number Theory
2012/4/18
A conjecture of Manin predicts the distribution of K-rational points on certain algebraic varieties defined over a number field K. In recent years, a method using universal torsors has been successful...
Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux
Computational Theoretical Challenges Counting Solid Standard Young Tableaux
2012/2/29
In how many ways can you place n chocolate pieces all of different sizes in an n by n chocolate box, in such a way that when you go from left to right and from top to bottom, there are no gaps AND the...
The Streaming Complexity of Cycle Counting, Sorting By Reversals, and Other Problems
Streaming Complexity Cycle Counting,
2012/12/3
In this paper we introduce a new technique for proving streaming lower bounds (and one-way communication lower bounds), by reductions from a problem called the Boolean Hidden Hypermatching problem (BH...
Exact Parameterized Multilinear Monomial Counting via k-Layer Subset Convolution and k-Disjoint Sum
Parameterized MultilinearConvolution
2012/12/3
We present new algorithms for exact multilinear k-monomial counting which is to compute the sum of coefficients of all degree-k multilinear monomials in a given polynomial P over a ring R described by...
Abstract: The main topic of this contribution is the problem of counting square-free numbers not exceeding $n$. Before this work we were able to do it in time (Comparing to the Big-O notation, Soft-O ...