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Let V be an r-dimensional vector space over an infinite field F of prime characteristic p, and let L n (V) denote the n-th homogeneous component of the free Lie algebra on V. We study the structure of L n (V) as a module for the general linear group GL r (F) when n = pk and k is not divisible by p and where n ≥ r. Our main result is an explicit 1-1… (More)

We first show that increasing trees are in bijection with set compositions , extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the linear span of set compositions (the twisted descent algebra). Among others, a number of enveloping algebra structures are… (More)

- M. Schocker
- 2008

We define the notion of weakly ordered semigroups. For this class of semigroups, we compute the radical of the semigroup algebras. This generalizes some results on left regular bands and on 0Hecke algebras.

In memory of our friend, colleague and former fellow student Manfred Schocker Summary. We provide a deterministic algorithm that constructs small point sets exhibiting a low star discrepancy. The algorithm is based on bracketing and on recent results on randomized roundings respecting hard constraints. It is structurally much simpler than the previous… (More)

- Manfred Schocker
- 2008

Let (W, S) be a finite Coxeter system. Tits defined an associative product on the set Σ of simplices of the associated Coxeter complex. The corresponding semigroup algebra is the Solomon-Tits algebra of W. It contains the Solomon algebra of W as the algebra of invariants with respect to the natural action of W on Σ. For the symmetric group S n , there is a… (More)

- Manfred Schocker
- Discrete Mathematics
- 2003

- Manfred Schocker
- 2008

A coplactic class in the symmetric group S n consists of all permutations in S n with a given Schensted Q-symbol, and may be described in terms of local relations introduced by Knuth. Any Lie element in the group algebra of S n which is constant on coplactic classes is already constant on descent classes. As a consequence, the intersection of the Lie… (More)

Based on a generalized ordering ∝ on a set X, Schensted's insertion mapping is defined on the set of words (W, ·) over the ordered alphabet (X, ∝). In this general framework, a transparent approach to various versions of the Robinson-Schensted correspondence and of invariant properties originally due to Schützenberger, Knuth, White e.a. is obtained.… (More)

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