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Roy Quintero

Abstract

The three-pile trick is a well-known card trick performed with a deck of 27 cards which dates back to the early seventeenth century at least and its objective is to uncover the card chosen by a volunteer. The main purpose of this research is to give a mathematical generalization of the three-pile trick for any deck of ab cards with a, b ≥ 2 any integers by means of a finite family of simple discrete functions. Then, it is proved each of these functions has just one or two stable fixed points. Based on this findings a list of 222 (three-pile trick)-type brand new card tricks was generated for either a package of 52 playing cards or any appropriate portion of it with a number of piles between 3 and 7. It is worth noting that all the card tricks on the list share the three main properties that have characterized the three-pile trick: simplicity, self-performing and infallibility. Finally, a general performing protocol, useful for magicians, is given for all the cases. All the employed math techniques involve naive theory of discrete functions, basic properties of the quotient and remainder of the division of integers and modular arithmetic.

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Teodoro Lara, Nelson Merentes, Roy Quintero and Edgar Rosales

Abstract

The main objective of this research is to characterize all the real polynomial functions of degree less than the fourth which are Jensen m-convex on the set of non-negative real numbers. In the first section, it is established for that class of functions what conditions must satisfy a particular polynomial in order to be starshaped on the same set. Finally, both kinds of results are combined in order to find examples of either Jensen m-convex functions which are not starshaped or viceversa.

Open access

Teodoro Lara, Roy Quintero and Edgar Rosales

Abstract

In this research we aim to explore some properties of m-convex functions from the point of view of functional equations or better, functional inequalities. So far studies of m- convexity have been devoted mainly to establish properties, inequalities and examples on the topic, but not to look at the problem from the perspective of functional inequalities.

Open access

Teodoro Lara, Janusz Matkowski, Nelson Merentes, Roy Quintero and Małgorzata Wróbel

Abstract

Functional inequalities generalizing m-convexity are considered. A result of a sandwich type is proved. Some applications are indicated.