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On multiplicities of points on Schubert varieties in Graszmannians II
Christian Krattenthaler
We prove a conjecture by Kreiman and Lakshmibai on a combinatorial description of multiplicities of points on Schubert varieties in Graszmannians in terms of certain sets of reflec…
Some new formulas for
Gert Almkvist, Christian Krattenthaler, Joakim Petersson
We show how to find series expansions for of the form , where S(n) is some polynomial in (depending on ). We prov…
A determinantal formula for the Hilbert series of one-sided ladder determinantal rings
Christian Krattenthaler, Martin Rubey
We give a formula that expresses the Hilbert series of one-sided ladder determinantal rings, up to a trivial factor, in form of a determinant. This allows the convenient computatio…
The Hilbert Series of Pfaffian Rings
Sudhir R. Ghorpade, Christian Krattenthaler
We give three determinantal expressions for the Hilbert series as well as the Hilbert function of a Pfaffian ring, and a closed form product formula for its multiplicity. An append…
Enumeration of lozenge tilings of hexagons with cut off corners
Mihai Ciucu, Christian Krattenthaler
Motivated by the enumeration of a class of plane partitions studied by Proctor and by considerations about symmetry classes of plane partitions, we consider the problem of enumerat…
A (conjectural) 1/3-phenomenon for the number of rhombus tilings of a hexagon which contain a fixed rhombus
Christian Krattenthaler
We state, discuss, provide evidence for, and prove in special cases the conjecture that the probability that a random tiling by rhombi of a hexagon with side lengths $2n+a,2n+b,2n+…