相关论文: On piecewise-linear homeomorphisms between distrib…

We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in (Kaibel and Pfetsch, 2008). These polytopes are the convex hulls of all 0/1-matrices with…

It is argued that the electron stripes as found in correlated oxides have to do with an unrecognized form of order. The manifestation of this order is the robust property that the charge stripes are at the same time anti-phase boundaries in…

Monotone path polytopes arise as a special case of the construction of fiber polytopes, introduced by Billera and Sturmfels. A simple example is provided by the permutahedron, which is a monotone path polytope of the standard unit cube. The…

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This…

We study the set of linear subspaces of a fixed dimension intersecting a given polytope. To describe this set as a semialgebraic subset of a Grassmannian, we introduce a Schubert arrangement of the polytope, defined by the Chow forms of the…

We apply to locally finite partially ordered sets a construction which associates a complete lattice to a given poset; the elements of the lattice are the closed subsets of a closure operator, defined starting from the concurrency relation.…

For two subsets S and T of a given lattice L, we define a relative distributive (modular) property over L, that underlies a large family including the usual class of distributive (modular) lattices. Our proposed class will be called…

For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…

Given a directed graph D = (N, A) and a sequence of positive integers 1 <= c_1 < c_2 < ... < c_m <= |N|, we consider those path and cycle polytopes that are defined as the convex hulls of simple paths and cycles of D of cardinality c_p for…

Bolytropes are bounded subsets of an affine building that consist of all points that have distance at most $r$ from some polytrope. We prove that the points of a bolytrope describe the set of all invariant lattices of a bolytrope order,…

The map which takes a square matrix $A$ to its polytrope is piecewise linear. We show that cones of linearity of this map form a polytopal fan partition of $\{R}^{n \times n}$, whose face lattice is anti-isomorphic to the lattice of…

We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star…

It will be shown that the toric ring of the chain polytope of a finite partially ordered set is an algebra with straightening laws on a finite distributive lattice. Thus in particular every chain polytope possesses a regular unimodular…

Skew polynomial rings were used to construct finite semifields by Petit in 1966, following from a construction of Ore and Jacobson of associative division algebras. In 1989 Jha and Johnson constructed the so-called cyclic semifields,…

In recent years, experimental and theoretical investigations have shown that anisotropic colloids can self-organise into ordered porous monolayers, where the interplay of localised bonding sites, so called patches, with the particle's shape…

Balister, the second author, Groenland, Johnston and Scott recently showed that there are asymptotically $C4^n/n^{3/4}$ many unordered sequences that occur as degree sequences of graphs. Combining limit theory for infinitely divisible…

The Multiple Choice Polytope (MCP) is the prediction range of a random utility model due to Block and Marschak (1960). Fishburn (1998) offers a nice survey of the findings on random utility models at the time. A complete characterization of…

The present thesis studies structural properties of non-crossing partitions associated to finite Coxeter groups from both algebraic and geometric perspectives. On the one hand, non-crossing partitions are lattices, and on the other hand, we…

Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study the orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which…

A linear-interval order is the intersection of a linear order and an interval order. For this class of orders, several structural results have been known. This paper introduces a new subclass of linear-interval orders. We call a partial…