Large Tableaux Research Articles

Rock Art Surveys in the Sudanese Eastern Desert: Results of the 2018–2019 Atbai Survey Project

The Sudanese Eastern Desert or the ‘Atbai’ is still largely unexplored from the point of view of rock art surveys. As part of the Atbai Survey Project’s fieldwork program, surveys conducted in 2018 and 2019 identified new rock art sites in the deserts around Gebel Nahoganet. Findings included a large tableau of a boat ‘fleet’ along with numerous sites yielding faunal rock art and surface remains. While a generalized boat motif is relatively commonplace in the corpus of rock art from Egypt and Nubia, this specific type of boat encountered in this distant desert exhibits a number of unique features. Notably, the tableau is carved within the walls of a natural tunnel and the features and manner of its execution have few parallels elsewhere. This contribution introduces the hypothesis that these boat motifs may have been the products of local Nubian groups including the A-Group horizon ( c. 3800–3100 BCE). [Formula: see text]

Representations of the Themes of Conflict and Peace within the Tradition of Well Dressing

This article explores the themes of conflict and peace as depicted within the English calendar custom of well dressing, a form of rural folk art where large tableaux are produced annually in the summer months using only natural materials pressed into a clay-filled board which is then sited at a local water source as an offering of gratitude for the essential gift of water. The custom is traditionally associated with the counties of Derbyshire and Staffordshire although it has spread further afield in recent years. The research includes both fieldwork (the author has been documenting the completed well dressings as well as their construction for a number of years, and in 2022 became a participant in the custom for the first time by joining the team of volunteer well dressers at the closest site to where he grew up) and study of archival sources including local newspaper reports to see how elements of the design process have changed over the years and been subject to influence by external trends.

Rigged configuration descriptions of the crystals B(∞) and B(λ) for special linear Lie algebras

The rigged configuration realization $RC(\infty)$ of the crystal $B(\infty)$ was originally presented as a certain connected component within a larger crystal. In this work, we make the realization more concrete by identifying the elements of $RC(\infty)$ explicitly for the $A_n$-type case. Two separate descriptions of $RC(\infty)$ are obtained. These lead naturally to isomorphisms $RC(\infty)\cong T(\infty)$ and $RC(\infty)\cong \bar{T}(\infty)$, i.e., those with the marginally large tableau and marginally large reverse tableau realizations of $B(\infty)$, that may be computed explicitly. We also present two descriptions of the irreducible highest weight crystal $B(\lambda)$ in terms of rigged configurations. These are obtained by combining our two descriptions of $RC(\infty)$, the two mentioned isomorphisms, and two existing realizations of $B(\lambda)$ that were based on $T(\infty)$ and $\bar{T}(\infty)$.

The Distributions of the Entries of Young Tableaux

Let T be a standard Young tableau of shape λ⊢k. We show that the probability that a randomly chosen Young tableau of n cells contains T as a subtableau is, in the limit n→∞, equal to fλ/k!, where fλ is the number of all tableaux of shape λ. In other words, the probability that a large tableau contains T is equal to the number of tableaux whose shape is that of T, divided by k!. We give several applications, to the probabilities that a set of prescribed entries will appear in a set of prescribed cells of a tableau, and to the probabilities that subtableaux of given shapes will occur. Our argument rests on a notion of quasirandomness of families of permutations, and we give sufficient conditions for this to hold.

Renaissance Artists in the Service of the People

That Artists played an active part in the civic affairs and the political crises of the fifteenth and sixteenth centuries comes as a startling revelation to many of us, so occupied with the pressing needs of peoples and governments today. Because none of the thousands of public pictures has come down to us, we have paid little attention to the written accounts and the few sketches and engravings made at the time. We have studied the close relationship of artists to the churches and to the courts of dukes and princes; but we have ignored the many services performed by artists for city councils, craft guilds, and merchants' organizations. Especially in France, Flanders, and England, many artists found more employment in preparing propaganda pictures for the government or the large civic clubs than they did in painting for the church or the aristocracy. Instead of adorning the walls of church or palace, they arranged large tableaux on the public streets for the entire populace. Instead of painting oil portra...