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Interlaced processes on the circle

Anthony P. Metcalfe, Neil O’Connell, Jon Warren (2009)

Annales de l'I.H.P. Probabilités et statistiques

When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of conjugacy classes of the unitary group, using a dynamical rule inspired by the RSK algorithm. Our motivation for doing this is to develop a parallel programme, on the circle, to some recently discovered connections in random matrix theory between reflected and conditioned...

Intertwining numbers; the n -rowed shapes

Hyoung J. Ko, Kyoung J. Lee (2007)

Czechoslovak Mathematical Journal

A fairly old problem in modular representation theory is to determine the vanishing behavior of the H o m groups and higher E x t groups of Weyl modules and to compute the dimension of the / ( p ) -vector space H o m A ¯ r ( K ¯ λ , K ¯ μ ) for any partitions λ , μ of r , which is the intertwining number. K. Akin, D. A. Buchsbaum, and D. Flores solved this problem in the cases of partitions of length two and three. In this paper, we describe the vanishing behavior of the groups H o m A ¯ r ( K ¯ λ , K ¯ μ ) and provide a new formula for the intertwining number for any...

Inverse zero-sum problems in finite Abelian p-groups

Benjamin Girard (2010)

Colloquium Mathematicae

We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible length over...

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