منابع مشابه
Weighted Lonesum Matrices and Their Generating Function
A lonesum matrix is a (0, 1)-matrix uniquely determined by its column and row sums, and the sum of its all entries is called the “weight” of it. The generating function of numbers of weighted lonesum matrices of each weight is given. A certain explicit formula for the number of weighted lonesum matrices is also proved.
متن کاملThe Zrank Conjecture and Restricted Cauchy Matrices
Abstract. The rank of a skew partition λ/μ, denoted rank(λ/μ), is the smallest number r such that λ/μ is a disjoint union of r border strips. Let sλ/μ(1 ) denote the skew Schur function sλ/μ evaluated at x1 = · · · = xt = 1, xi = 0 for i > t. The zrank of λ/μ, denoted zrank(λ/μ), is the exponent of the largest power of t dividing sλ/μ(1 ). Stanley conjectured that rank(λ/μ) = zrank(λ/μ). We sho...
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In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of compressed sensing involve a data-acquisitio...
متن کاملThe enumeration of some restricted matrices
Our purpose’ is to show that these enumeration problems may be reduced to a more familiar type of problem involving the enumeration of restricted lattice paths. Moreover, the reduced problems are amenable to first and last passage decomposition methods (see [S, 63 and Section 2), so that we obtain in this way solutions to the original matrical problems. Carlitz [3] has considered the case t 2 w...
متن کاملClique Matrices for Statistical Graph Decomposition and Parameterising Restricted Positive Definite Matrices
We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters, defined as wellconnected subsets of vertices. The decomposition is based on a statistical description which encourages clusters to be well connected and few...
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ژورنال
عنوان ژورنال: Annales Mathematicae et Informaticae
سال: 2018
ISSN: 1787-5021,1787-6117
DOI: 10.33039/ami.2018.10.001