Gröbner bases for permutations and oriented trees

Cambrian Hopf Algebras

Cambrian trees are oriented and labeled trees which fulfill local conditions around each node generalizing the conditions for classical binary search trees. Based on the bijective correspondence between signed permutations and leveled Cambrian trees, we define the Cambrian Hopf algebra generalizing J.-L. Loday and M. Ronco’s algebra on binary trees. We describe combinatorially the products and ...

Gröbner Bases of Oriented Grassmann Manifolds

For n = 2 − 4, m > 2, we determine the cup-length of H∗(G̃n,3;Z/2) by finding a Gröbner basis associated with a certain subring, where G̃n,3 is the oriented Grassmann manifold SO(n + 3)/SO(n)× SO(3). As an application, we provide not only a lower but also an upper bound for the LS-category of G̃n,3. We also study the immersion problem of G̃n,3.

On Path diagrams and Stirling permutations

Any ordinary permutation τ ∈ Sn of size n, written as a word τ = τ1 . . . τn, can be locally classified according to the relative order of τj to its neighbours. This gives rise to four local order types called peaks (or maxima), valleys (or minima), double rises and double falls. By the correspondence between permutations and binary increasing trees the classification of permutations according ...

MATH536A Paper: Gröbner Bases

An introduction to Gröbner bases and some of their uses in affine algebraic geometry.

Gröbner bases for codes