Diffraction physics with ALICE at the LHC

The ALICE experiment is equipped with a wide range of detectors providing excellent tracking and particle identification in the central region, as well as forward detectors with extended pseudorapidity coverage, which are well suited for studying diffractive processes. Cross section measurements of single and double diffractive processes performed by ALICE in pp collisions at $\sqrt{s}=0.9,~2.76,~7$~TeV will be reported. Currently, ALICE is studying double-gap events in pp collisions at $\sqrt{s}=7$~TeV, which give an insight into the central diffraction processes: current status and future perspectives will be discussed. The upgrade plans for diffraction studies, further extending the pseudorapidity acceptance of the ALICE setup for the forthcoming Run 2 of the LHC, will be outlined.Comment: 8 pages 5 figures, proceedings of talk given at XXXth International Workshop on High Energy Physics "Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects", June 23-27, 2014, in Protvino, Moscow region, Russi

Crucial Words and the Complexity of Some Extremal Problems for Sets of Prohibited Words

We introduced the notation of a set of prohibitions and give definitions of a complete set and a crucial word with respect to a given set of prohibitions. We consider 3 particular sets which appear in different areas of mathematics and for each of them examine the length of a crucial word. One of these sets is proved to be incomplete. The problem of determining lengths of words that are free from a set of prohibitions is shown to be NP-complete, although the related problem of whether or not a given set of prohibitions is complete is known to be effectively solvable.Comment: 16 page

Characterization of Balanced Coherent Configurations

Let $G$ be a group acting on a finite set $\Omega$. Then $G$ acts on $\Omega\times \Omega$ by its entry-wise action and its orbits form the basis relations of a coherent configuration (or shortly scheme). Our concern is to consider what follows from the assumption that the number of orbits of $G$ on $\Omega_i\times \Omega_j$ is constant whenever $\Omega_i$ and $\Omega_j$ are orbits of $G$ on $\Omega$. One can conclude from the assumption that the actions of $G$ on ${\Omega_i}$'s have the same permutation character and are not necessarily equivalent. From this viewpoint one may ask how many inequivalent actions of a given group with the same permutation character there exist. In this article we will approach to this question by a purely combinatorial method in terms of schemes and investigate the following topics: (i) balanced schemes and their central primitive idempotents, (ii) characterization of reduced balanced schemes