Adrián Muñoz Perera

A set of dice is intransitive if contains dice with the property that given a particular die in the set, some dice roll higher more than half the time, but also others roll lower half the time. This means that the relation between the dice "die A beats die B" is not transitive. Obtaining such a set of dice is difficult in general, the structure of these sets is not very intuitive.

Some particular cases have been produced over time, for several number of players and several number of faces in the dice. In this paper, a general expression for a set of instransitive dice of any given size is provided, and the the probability of one die rolling higher than other in the set is explicitly computed. This novel general expression is simple yet has some complex symmetries that help understand this beautiful mathematical curiosity.

Next, some particular cases of these set of dice are depicted, these are some dice that can be built using tethraedra and the usual cubic dice shape.

N=4

A:	1	8	12	14
B:	2	5	11	15
C:	3	6	9	16
D:	4	7	10	13

It can be verified that B>A, C>B, D>C y A>D, where "X>Y" means the probability of die X rolling higher than die Y is bigger than the probability of die Y rolling higher than die X.

N=6

A:	1	12	17	22	28	33
B:	2	7	18	23	29	34
C:	3	8	13	24	30	35
D:	4	9	14	19	25	36
E:	5	10	15	20	26	31
F:	6	11	16	21	27	32

Again B>A, C>B, D>C, E>D, F>E y A>F.

You can download the paper in this link.

Final project corresponding to my Master's Degree in ICT Research and Innovation (i2-ICT). A computational analysis on spectral representation (in the domain of frequencies) of several types of gaussian processes in supported in bounded domains. Kernels such as brownian motion, brownian bridge, Ornstein-Uhlenbeck, Radial Basis Function (RBF), Matérn and exponential are studied.

Master's Degree in Mathematics and Applications' final project. On regularization of functional data and its embedding in optimal classification rules in the continuous time gaussian process framework.

Final project corresponding to Double Degree on Mathematics and Computer Science. The codification of shape of objects in terms of directional data is addressed, with an application to a real world classification problem. Included in the proceedings of the 27th International Conference on Artificial Neural Networks, ICANN 2018, held in Rhodes, Greece, in October 2018. Part of the Lecture Notes in Computer Science book series (LNCS, volume 11139). Also part of the Theoretical Computer Science and General Issues book sub series (LNTCS, volume 11139)