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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)

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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