Permutation Statistics on the Alternating Group

Let $A_n\subseteq S_n$ denote the alternating and the symmetric groups on $1,...,n$. MacMahaon's theorem, about the equi-distribution of the length and the major indices in $S_n$, has received far reaching refinements and generalizations, by Foata, Carlitz, Foata-Schutzenberger, Garsia-Gessel and followers. Our main goal is to find analogous statistics and identities for the alternating group $A_{n}$. A new statistic for $S_n$, {\it the delent number}, is introduced. This new statistic is involved with new $S_n$ equi-distribution identities, refining some of the results of Foata-Schutzenberger and Garsia-Gessel. By a certain covering map $f:A_{n+1}\to S_n$, such $S_n$ identities are `lifted' to $A_{n+1}$, yielding the corresponding $A_{n+1}$ equi-distribution identities.Comment: 45 page

Generalized Einstein relation for disordered semiconductors - implications for device performance

The ratio between mobility and diffusion parameters is derived for a Gaussian-like density of states. This steady-state analysis is expected to be applicable to a wide range of organic materials (polymers or small molecules) as it relies on the existence of quasi-equilibrium only. Our analysis shows that there is an inherent dependence of the transport in trap-free disordered organic-materials on the charge density. The implications for the contact phenomena and exciton generation rate in light emitting diodes as well as channel-width in field-effect transistors is discussed

On Degrees in the Hasse Diagram of the Strong Bruhat Order

For a permutation $\pi$ in the symmetric group $S_n$ let the {\it total degree} be its valency in the Hasse diagram of the strong Bruhat order on $S_n$, and let the {\it down degree} be the number of permutations which are covered by $\pi$ in the strong Bruhat order. The maxima of the total degree and the down degree and their values at a random permutation are computed. Proofs involve variants of a classical theorem of Tur\'an from extremal graph theory.Comment: 14 pages, minor corrections; to appear in S\'em. Lothar. Combi

Dance on screen

This thesis explores dance on screen from the artist's point of view following the making of the video GAIA - Mysterious Rhythms (20 min,Digital Betacam). The video and the thesis together form the PhD submission. The interaction of practice and theory, through a process of creative work, analysis and reflection resulted in the structuring of a model with which I claim the autonomy of dance on screen as a hybrid art form, a form which like other creative forms, such as painting, sculpture or even dance, has its own particular aesthetic qualities and limits. This thesis proposes that dance as a live form ceases to exist in the process of its recreation as a screen form. The argument about dance on screen is based not within the context of contemporary live dance, but within the contexts of film/video, screen choreography and performance, including 'performative' texts and art as performance engaging both artists and viewers. To locate dance on screen in a contemporary framework, I refer to central developments issuing from the television series Dance for the Camera produced by BBC2 & the Arts Council and the IMZ/Dance Screen international festivals. I approach choreography in screen terms thereby referring to the expression of movement in the broader sense, including performance, body language, the motion of objects and natural events, and rhythms and movements created via film/video technology. The moving body on screen is also utilised for the expression of mythical journeys as in Gaia. Overall, this thesis demonstrates that dance on screen, originating from the contexts of modem and post-modem art and culture, constitutes a unique art form and phenomenon reflecting current concerns with the notions of hybridity and performance