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The (Combinatorial) Object Server: A mathematical tool for producing lists of combinatorial objects.

Plato's diamond after 24 centuries... Hidden symmetries of Plato's Meno figure throw new light on topics in finite geometry, finite group theory, and combinatorics.

European site Canadian mirror INRIA Search Encyclopedia of Combinatorial Structures Algorithms Project INRIA Welcome People Publications AofA Software Seminars Books ECS Introduction/ Example Search Submit a new structure Encyclopedia Package Help For more information Introduction This encyclopedia of combinatorial structures has been written by Stephanie Petit. It ambitions to be seen as a ...

Personal Web pages of combinatorialists, graph theorists, and others with an interest in discrete mathematics, from the World Combinatorial Exchange ...

The Web page of the British Combinatorial Committee, containing information for combinatorial mathematicians in the United Kingdom and many links ...

CATS: Combinatorial Algorithms Test Sets Mission: To facilitate experimental research by standardizing common benchmarks, providing a mechanism for their evolution, and making them easily accessible and usable; and identifying significant open questions in the design of good test sets and the assessment of performance of existing algorithms. To facilitate algorithm selection for applications by ...

Venn Diagram Survey: combinatorial facts, beautiful figures, n=3 and beyond ...

Lengthy discussion of combinatorics, from The Mathematical Atlas.

Handbook of Combinatorial Designs Welcome to the home page for The CRC Handbook of Combinatorial Designs (ISBN: 0-8493-8948-8). The following pages are currently available. Table of Contents Acknowledgments New Results. These are results that have appeared since the Handbook was sent to press. Errata in the Handbook of Combinatorial Designs. Ordering Information from CRC. Back to Jeff Dinitz ...

Web-based resources for design theory and related areas ...

Introduction | Results | Table | Generator matrices for caps | Introduction A cap in PG(k-1, q) is a set of points no three of which are collinear. If we write the n points as columns of a matrix we obtain a (k, n)-matrix such that every set of three columns is linearly independent, hence the generator matrix of a linear orthogonal array of strength 3. This is a check matrix of a linear code with ...

La Jolla Covering Repository A (v, k, t)-covering design is a collection of k-element subsets, called blocks, of {1, 2, ..., v}, such that any t-element subset is contained in at least one block. This site contains (v, k, t)-coverings with vgordon@ccrwest.org. These coverings were constructed using techniques from the paper New Constructions for Covering Designs, by myself, Greg Kuperberg, and Oren ...

An algebraic theory of chord structures ...

Web page supporting the book Extremal Combinatorics: list of misprints, further exercises and problems, links, etc.

Algebraic Combinatorics Via Finite Group Actions A. Betten, H. Fripertinger, A. Kerber August 28, 2001 Actions Actions of groups Orbits Stabilizers Fixed points Examples Cosets The Cauchy-Frobenius Lemma The permutation character The Cauchy-Frobenius Lemma 2 Similar Actions Exercises Bilateral classes, symmetry classes of mappings Double Cosets Action on k-subsets Sylows Theorem Products of ...

Topics in Mathematics Combinatorics Algebraic Combinatorics Via Finite Group Actions ADD. KEYWORDS: Lecture Notes Algorithms Project at INRIA ADD. KEYWORDS: Publications, Analysis of Algorithms, Software, Seminars, Books, On-line Encyclopedia AMOF: The Amazing Mathematical Object Factory ADD. KEYWORDS: Subsets, Combinations, Permutations, 8-Queens Problem, Pentominoes, Permutations of a ...

This web page contains a table giving the lengths of the shortest known Golomb rulers for up to 150 marks. The values for 23 marks or less are known to be optimal. For the actual rulers see known optimal rulers best rulers from projective plane construction best rulers from affine plane construction Table of lengths of shortest known Golomb rulers marks length found by proved by comments 1 0 ...

The cutting sticks problem The name of the problem comes from a populair by which the problem can be stated: You are given k sticks with integer length of which the total length of sums up to n(n+1)/2. Non of the sticks are shorter than n. Can you always cut them into sticks with length 1, 2, upto n, no matter the number of the sticks and their lenghts. Obvious assumptions are that you are not ...

Mathematical blackjack and the Steiner system S(5, 6, 12) by David Joyner and Ann Luers, Math Dept, USNA This web page has been corrected and expanded. Click here for the new version. Click here for the MAPLE implementation of Curtis' kitten (for any labeling and any MINIMOG). Click here for the MAPLE implementation of Curtis' kitten (for the shuffle labeling) and to play mathematical blackjack ...

My research interests at the present time are in the area of classification of combinatorial designs of various different sorts. In some cases I have been able to classify the designs completely and where this has been possible I have stored the designs on disc. They can be accessed via the Table below. These files will be updated at intervals, as I find the time. The `smallest' parameter set of ...

Lecture Notes Here is a set of lecture notes called East Side, West Side, ... , which are about the generation of combinatorial objects and Maple programming that gets the job done. These notes formed the basis of half of a junior course that I have recently given, and they are about 60 pages long (Version of August 15, 1999). You can download them as an Adobe Acrobat file. By doing so you are ...

Dodecahedral Faces of M12 by Ann Luers This paper constitutes part of my honors thesis written in spring 1997 at the USNA, advisor Assoc Prof. David Joyner. Groups are objects in mathematics that measure symmetry in nature. A group is a set with a binary operation that has an inverse, an identity and is associative. For example, a clock has 12-fold symmetry. A more unusual group is a sporadic, ...

Enumeration of the Binary Trees (Catalan numbers). For each number of nodes, n, there is a certain number of possible binary tree configurations. These numbers form a sequence of integers with respect to n. A useful way to describe an integer sequence is to construct a generating function: (1) whose coefficients bi are the sequence. B(x) is power series over a purely formal variable x. We are ...