q-Hook length formulas for colored labeled forests

The major index has been deeply studied from the early 1900s and recently has been generalized in different directions, such as the case of labeled forests and colored permutations. In this thesis we define new types of labelings for forests in which the labels are colored integers. We extend the definition of the flag-major index for these labelings and we present an analogue of well known major index hook length formulas. Finally, this study (which has just apparently a simple combinatoric nature) allows us to show a notion of duality for two particular families of groups obtained from the product G(r,n)×G(r,m).

Cheering the soul: Ibn Qāḍī Baʿlabakk’s Mufarriḥ an-Nafs. Arabic edition, english translation, study and glossaries

The Mufarriḥ an-nafs (Soul-Cheerer), attributed to Badr ad-Dīn Muẓaffar Ibn Qāḍī Baʿlabakk, who served under the Ayyubids as the Chief Medical Officer of Damascus in the mid-13th century, was written as a comprehensive guide for physicians outlining different approaches to cheering the soul. The tractate is divided into ten chapters, which explore the nature of the soul, its distinction to the body as well as their connection through sensorial perception. Ibn Qāḍī Baʿlabakk distinguishes the bodily senses – hearing, vision, smell, taste, touch – and the inner senses, which he sees as stimulated through activities such as hunting and engagement in poetry and the sciences. The seventh chapter of the Mufarriḥ an-nafs includes an extended encyclopedia on materia medica as well as dispensatory of simple and compound drugs, which is devoted to treating the soul and remains unparalleled in the history of Islamicate medicine. My doctoral dissertation offers a complete recension and translation of the Mufarriḥ an-nafs based on a stemma codicum drawn from the seventeen extant text witnesses. The dissertation contextualizes the work, its author as well as sources, and features a text commentary that seeks to enable the reader to easily place and understand the Mufarriḥ an-nafs within the tradition of Galenic medicine. The glossaries on materia medica found at the end of the dissertation are aimed at facilitating access to the pharmacological dispensatory included in the seventh chapter.