6,777 research outputs found
Rational Shi tableaux and the skew length statistic
International audienceWe define two refinements of the skew length statistic on simultaneous core partitions. The first one relies on hook lengths and is used to prove a refined version of the theorem stating that the skew length is invariant under conjugation of the core. The second one is equivalent to a generalisation of Shi tableaux to the rational level of Catalan combinatorics. We prove that the rational Shi tableau is injective. Moreover we present a uniform definition of the rational Shi tableau for Weyl groups and conjecture injectivity in the general case
Growth diagrams, Domino insertion and Sign-imbalance
We study some properties of domino insertion, focusing on aspects related to
Fomin's growth diagrams. We give a self-contained proof of the semistandard
domino-Schensted correspondence given by Shimozono and White, bypassing the
connections with mixed insertion entirely. The correspondence is extended to
the case of a nonempty 2-core and we give two dual domino-Schensted
correspondences. We use our results to settle Stanley's `2^{n/2}' conjecture on
sign-imbalance and to generalise the domino generating series of Kirillov,
Lascoux, Leclerc and Thibon.Comment: 24 page
Stationary quasi-perfect equilibrium partitions constitute the recursive core
We present sucient conditions for the implementation of the (pessimistic) recursive core (Kóczy, 2007) in discrete partition function form games using a modified version of the sequential coalition formation game by Bloch (1996) extending the results of Kóczy (2008) and - in a slightly different setup - Huang and Sjöström (2006) to games with empty residual cores (respectively, to games that are not r-balanced).Economics (Jel: A)
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