6,348 research outputs found

    The Asymptotic Number of Irreducible Partitions

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    A partition of [1, n] = {1,..., n} is called irreducible if no proper subinterval of [1, n] is a union of blocks. We determine the asymptotic relationship between the numbers of irreducible partitions, partitions without singleton blocks, and all partitions when the block sizes must lie in some specified set

    Asymptotic enumeration of non-crossing partitions on surfaces

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    We generalize the notion of non-crossing partition on a disk to general surfaces with boundary. For this, we consider a surface S and introduce the number CS(n) of noncrossing partitions of a set of n points laying on the boundary of SPostprint (author's final draft

    Linear versus spin: representation theory of the symmetric groups

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    We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition Îľ\xi with analogous normalized linear characters evaluated on the double partition D(Îľ)D(\xi). We also relate some natural filtration on the usual (linear) Kerov-Olshanski algebra of polynomial functions on the set of Young diagrams with its spin counterpart. Finally, we give a spin counterpart to Stanley formula for the characters of the symmetric groups.Comment: 41 pages. Version 2: new text about non-oriented (but orientable) map

    Relativistic Quantum Mechanics - Particle Production and Cluster Properties

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    This paper constructs relativistic quantum mechanical models of particles satisfying cluster properties and the spectral condition which do not conserve particle number. The treatment of particle production is limited to systems with a bounded number of bare-particle degrees of freedom. The focus of this paper is about the realization of cluster properties in these theories.Comment: 36 pages, Late

    On the Mullineux involution for Ariki-Koike algebras

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    This note is concerned with a natural generalization of the Mullineux involution for Ariki-Koike algebras. Using a result of Fayers together with previous results by the authors, we give an efficient algorithm for computing this generalized Mullineux involution. Our algorithm notably does not involve the determination of paths in affine crystals.Comment: 17 page
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