32 research outputs found
Intertwining connectivity in matroids
Let be a matroid and let , , and be subsets of the ground
set such that the smallest separation that separates from has order
and the smallest separation that separates from has order . We prove
that if is sufficiently large, then there is an
element of such that, in one of or , both
connectivities are preserved
Intertwining connectivities in representable matroids
Let be a representable matroid and subsets of the ground set such that the smallest separation that separates from has order , and the smallest separation that separates from has order . We prove that if is sufficiently large, then there is an element such that in one of and both connectivities are preserved. For matroids representable over a finite field we prove a stronger result: we show that we can remove such that both a connectivity and a minor of are preserved
Towards a matroid-minor structure theory
This paper surveys recent work that is aimed at generalising the results and techniques of the Graph Minors Project of Robertson and Seymour to matroids
On packing 3-connected restrictions into 3-connected matroids
Let M1,M2,...,Mn be 3-connected restrictions of a 3-connected matroid M on disjoint ground sets E1,E2,...,En, respectively. This paper proves that M has a 3-connected minor N that contains E1 UE2 U ··· UEn, has its restriction to each Ei, being Mi, and has at most 2n - 2 additional elements
Quantum Knizhnik-Zamolodchikov Equation, Totally Symmetric Self-Complementary Plane Partitions and Alternating Sign Matrices
We present multiresidue formulae for partial sums in the basis of link
patterns of the polynomial solution to the level 1 U_q(\hat sl_2) quantum
Knizhnik--Zamolodchikov equation at generic values of the quantum parameter q.
These allow for rewriting and generalizing a recent conjecture [Di Francesco
'06] connecting the above to generating polynomials for weighted Totally
Symmetric Self-Complementary Plane Partitions. We reduce the corresponding
conjectures to a single integral identity, yet to be proved
Real Algebraic Geometry With A View Toward Systems Control and Free Positivity
New interactions between real algebraic geometry, convex optimization and free non-commutative geometry have recently emerged, and have been the subject of numerous international meetings. The aim of the workshop was to bring together experts, as well as young researchers, to investigate current key questions at the interface of these fields, and to explore emerging interdisciplinary applications