6,348 research outputs found
The Asymptotic Number of Irreducible Partitions
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
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
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
with analogous normalized linear characters evaluated on the double
partition . 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)
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Relativistic Quantum Mechanics - Particle Production and Cluster Properties
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
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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