A bijective proof of the product formula for the principal specialization of super Schur functions (also called hook Schur functions) is given using the combinatorial description of super Schur functions in terms of certain tableaux due to Berele and Regev. Our bijective proof is based on the Hillman–Grassl algorithm and a modified version of Schützenberger’s jeu de taquin. We then explore the ...

The jeu de taquin process produced a standard Young tableau from a skew standard Young tableau by shifting its entries to the northwest. We generalize this process to posets: certain partial numberings of any poset are shifted upward. A poset is said to have the jeu de taquin property if the numberings resulting from this process do not depend upon certain choices made during the process. Young...

Littelmann has given a combinatorial model for the characters of representations of semisimple Lie algebras, in terms of certain paths traced in the space of (rational) weights. From it, a description of the decomposition of tensor products can be derived that generalises the Littlewood-Richardson rule (the latter is valid in type A n only). We present a new combinatorial construction that expr...

We present an adaptation of jeu de taquin and promotion for arbitrary fillings of moon polyominoes. Using this construction we show various symmetry properties of such fillings taking into account the lengths of longest increasing and decreasing chains. In particular, we prove a conjecture of Jakob Jonsson. We also relate our construction to the one recently employed by Christian Krattenthaler,...

Some new relations on skew Schur function differences are established both combinatorially using Schützenberger’s jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences of skew Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions confirms the validi...

Bien que le jeu vidéo soit une technologie connue pour se divertir et largement adoptée, la question des émotions, de l'immersion et du sommeil en lien avec le jeu vidéo reste discrète. La quasi-totalité des joueurs ont un jour ressenti une émotion soit positive (joie), soit négative (colère) en jouant. Et si ces émotions pouvaient être utilisées comme source de gameplay (manière de jouer) ? Po...

We present a proof of a Littlewood–Richardson rule for the K-theory of odd orthogonal Grassmannians OG.n; 2n C 1/, as conjectured by Thomas–Yong (2009). Specifically, we prove that rectification using the jeu de taquin for increasing shifted tableaux introduced there, is well-defined and gives rise to an associative product. Recently, Buch–Ravikumar (2012) proved a Pieri rule for OG.n; 2nC1/ th...

We give a bijection between the symmetric group Sn, and the set of standard Young tableaux of rectangular shape mn, m > n, that have order n under jeu de taquin promotion.

Le jeu de Go est un ancien jeu chinois. Il est très populaire en Corée, au Japon et en Chine. Les générations successives de joueurs de Go ont accumulé une expérience énorme du jeu tout au long de son histoire. Pour donner une idée de la somme des connaissances sur ce jeu, on peut citer les historiens chinois qui écrivent souvent que c'est Yao, un empereur semi-mythique du 23 siècle avant J.-C....

We describe jeu de paume, a small suite of security tools specially geared toward the protection of data on handheld devices. The components of jeu de paume are: (1) A visual password system adapted to stylus-based data entry; (2) An encryption system for credit-card numbers using low-entropy keys; and (3) A signature scheme with a cryptographic mechanism for deterring theft.