1,138 research outputs found
Broken circuit complexes and hyperplane arrangements
We study Stanley-Reisner ideals of broken circuits complexes and characterize
those ones admitting a linear resolution or being complete intersections. These
results will then be used to characterize arrangements whose Orlik-Terao ideal
has the same properties. As an application, we improve a result of Wilf on
upper bounds for the coefficients of the chromatic polynomial of a maximal
planar graph. We also show that for an ordered matroid with disjoint minimal
broken circuits, the supersolvability of the matroid is equivalent to the
Koszulness of its Orlik-Solomon algebra.Comment: 21 page
Enumeration of PLCP-orientations of the 4-cube
The linear complementarity problem (LCP) provides a unified approach to many
problems such as linear programs, convex quadratic programs, and bimatrix
games. The general LCP is known to be NP-hard, but there are some promising
results that suggest the possibility that the LCP with a P-matrix (PLCP) may be
polynomial-time solvable. However, no polynomial-time algorithm for the PLCP
has been found yet and the computational complexity of the PLCP remains open.
Simple principal pivoting (SPP) algorithms, also known as Bard-type algorithms,
are candidates for polynomial-time algorithms for the PLCP. In 1978, Stickney
and Watson interpreted SPP algorithms as a family of algorithms that seek the
sink of unique-sink orientations of -cubes. They performed the enumeration
of the arising orientations of the -cube, hereafter called
PLCP-orientations. In this paper, we present the enumeration of
PLCP-orientations of the -cube.The enumeration is done via construction of
oriented matroids generalizing P-matrices and realizability classification of
oriented matroids.Some insights obtained in the computational experiments are
presented as well
Tensor structure from scalar Feynman matroids
We show how to interpret the scalar Feynman integrals which appear when
reducing tensor integrals as scalar Feynman integrals coming from certain nice
matroids.Comment: 12 pages, corrections suggested by referee
- …