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Solid Converter PDF is document reconstruction software from Solid Documents which converts PDF files to editable formats. Originally released for the Microsoft Windows operating system, a Mac OS X version was released in 2010. The current versions are Solid Converter PDF 9.0 for Windows and Solid PDF to Word for Mac 2.1.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
If the order m > 2 then m must be a multiple of 4. Given an Hadamard matrix of order 4a in standardized form, remove the first row and first column and convert every −1 to a 0. The resulting 0–1 matrix M is the incidence matrix of a symmetric 2 − (4a − 1, 2a − 1, a − 1) design called an Hadamard 2-design. [8]
Geometric combinatorics is a branch of mathematics in general and combinatorics in particular. It includes a number of subareas such as polyhedral combinatorics (the study of faces of convex polyhedra), convex geometry (the study of convex sets, in particular combinatorics of their intersections), and discrete geometry, which in turn has many applications to computational geometry.
Bijection between 3 bit binary numbers and compositions of 4. A weak composition of an integer n is similar to a composition of n, but allowing terms of the sequence to be zero: it is a way of writing n as the sum of a sequence of non-negative integers. As a consequence every positive integer admits infinitely many weak compositions (if their ...
The Fano matroid, derived from the Fano plane.Matroids are one of many kinds of objects studied in algebraic combinatorics. Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
Extremal combinatorics is a field of combinatorics, which is itself a part of mathematics.Extremal combinatorics studies how large or how small a collection of finite objects (numbers, graphs, vectors, sets, etc.) can be, if it has to satisfy certain restrictions.
Smallpdf is a Swiss online web-based PDF software, founded in 2013. [2] It offers free version with limited features to compress, convert and edit PDF documents. [3] And its paid version offers advanced features like OCR, compress, and more. [4]
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