Abstract:
Why use magic for teaching combinatory, algorithms and finally informatics basis as tables, control structure, loops and recursive function? Magicians know that once the surprise has worn off, the audience will seek to understand how the trick works. The aim of every teacher is to interest their students, and a magic trick will lead them to ask ‘how?’ and ‘why?’ and ‘how can I create one myself?’ In this article we consider a project I presented in 2009, the subject of which was ‘How many riffle shuffles does exist from a N card deck? Find the composition of each possible riffle shuffle’. The aim of the paper is not only to describe the project scope, the students’ theoretical studies, their approach to this problem and their computer realizations, but also to give ideas for a course or project using pedagogy. That is why only remarkable students’ realizations are shown. In order to complete the given project, the students must answer three steps: the first one is to answer to the following question: “how can I find all possible riffle shuffles with few cards? (for exe*ample 3, 4 or 5 cards) the second one (to go further ) is to answer to the following question “how can I generalize this solution through an algorithm?” the last one (to obtain the results!) is to program the algorithm with a recursive and a non-recursive solution). Each step of the Matlab? solution code is associated with an informatics basis. Whatever the student's professional ambitions, they will be able to see the impact that originality and creativity have when combined with an interest in one’s work. That’s why, two ameliorations of the ‘basic’ algorithm are proposed and a study of the gain thanks to these ameliorations is done. The students know how to “perform” a magic trick for their family and friends thanks to the use of riffle shuffle in Gilbreath’s principles, a trick that they will be able to explain and so enjoy a certain amount of success with. Sharing a mathematical/informatics demonstration is not easy and the fact that they do so means that they will have worked on and understood and are capable of explaining this knowledge. Isn’t this the aim of all teaching?

Abstract:
There are many links between mathematics and magic: on the one hand, it is usual to see how mathematical principles apply in order to create magic tricks and, on the other hand, several specific techniques in magic give rise to mathematical models providing interesting properties in recreational mathematics. In this work we show this duality relating the famous Josephus problem and its variants with specific card shuffles used in some card tricks. In order to display the educational nature of this problem, we also suggest some teaching activities to develop in a classroom.

Abstract:
The goal of our work is to study the spaces of primitive elements of the Hopf algebras associated to the permutaedra and the associaedra. We introduce the notion of shuffle and preshuffle bialgebras, and compute the subpaces of primitive elements associated to these algebras. These spaces of primitive elements are free objects for some types of algebras which we describe in terms of generators and relations.

Abstract:
In this paper we generalize the well-known construction of shuffle product algebras by using mixable shuffles, and prove that any free Baxter algebra is isomorphic to a mixable shuffle product algebra. This gives an explicit construction of the free Baxter algebra, extending the work of Rota and Cartier.

Abstract:
There exist very lucid explanations of the combinatorial origins of rational and algebraic functions, in particular with respect to regular and context free languages. In the search to understand how to extend these natural correspondences, we find that the shuffle product models many key aspects of D-finite generating functions, a class which contains algebraic. We consider several different takes on the shuffle product, shuffle closure, and shuffle grammars, and give explicit generating function consequences. In the process, we define a grammar class that models D-finite generating functions.

Abstract:
It is proved that Drinfel'd's pentagon equation implies the generalized double shuffle relation. As a corollary, an embedding from the Grothendieck-Teichm\"uller group $GRT_1$ into Racinet's double shuffle group $DMR_0$ is obtained, which settles the project of Deligne-Terasoma. It is also proved that the gamma factorization formula follows from the generalized double shuffle relation.

Abstract:
In this paper, we introduce certain new features of the shuffle algebra, that will allow us to obtain explicit formulas for the isomorphism between its Drinfeld double and the elliptic Hall algebra.

Abstract:
Wikipedia introduced a new social function "wiki-thanks". "Wiki-thanks" enable editors to send thanks to other editors' contributions. In this paper, we aim to investigate this new social tool from different cultural perspectives. To achieve this goal, we analyze "wiki-thanks" log events and compared the English, German, Spanish, Chinese, Japanese, Korean, and Finish language Wikipedias.

Abstract:
The Thorp shuffle is defined as follows. Cut the deck into two equal piles. Drop the first card from the left pile or the right pile according to the outcome of a fair coin flip; then drop from the other pile. Continue this way until both piles are empty. We show that the mixing time for the Thorp shuffle with $2^d$ cards is polynomial in $d$.

Abstract:
The goal of this article is to give an elementary proof of the double shuffle relations directly for the Goncharov and Manin motivic multiple zeta values. The shuffle relation is straightforward, but for the stuffle we use a modification of a method first introduced by P. Cartier for the purpose of proving stuffle for the real multiple zeta values via integrals and blow-up sequences.