A compressed polytope is an integral convex polytope any of whose reverse lexicographic initial ideals is squarefree. A sufficient condition for a (0, 1)-polytope to be compressed will be presented. One of its immediate consequences is that the class of compressed (0, 1)-polytopes includes (i) hypersimplices, (ii) order polytopes of finite partially ordered sets, and (iii) stable polytopes of p...

A positroid is a special case of realizable matroid that arose from the study totally nonnegative part Grassmannian by Postnikov. In this paper, we facets its polytope and independent set polytope. This allows one to describe bases sets directly decorated permutation, bypassing use Grassmann necklace. We also criterion for determining whether given cyclic interval flat or not using then show ho...

We investigate the question of whether any d-colorable simplicial d-polytope can be octahedralized, i.e., subdivided to a d-dimensional geometric cross-polytopal complex. give positive answer in dimension 3, with additional property that octahedralization introduces no new vertices on boundary polytope.

Epitope-based vaccination strategies designed to induce tumor-specific CD8 CTL are being widely considered for cancer immunotherapy. Here we describe a recombinant poxvirus vaccine that codes for ten HLA-A2-restricted epitopes derived from five melanoma Ags conjoined in an artificial polyepitope or polytope construct. Target cells infected with the melanoma polytope vaccinia were recognized by ...

A (convex) polytope is the convex hull of finitely many points in Rd. Alternatively, a polytope can be defined as the bounded intersection of finitely many halfspaces, that is, a polytope is the (bounded) solution set of a system of linear equations and inequalities. (This latter fact is the main non-geometric reason why people are interested in polytopes—linear systems are everywhere.) The mai...

For two elements $v$ and $w$ of the symmetric group $\mathfrak{S}_n$ with $v\leq w$ in Bruhat order, interval polytope $Q_{v,w}$ is convex hull points $(z(1),\ldots,z(n))\in \mathbb{R}^n$ z\leq w$. It known that moment map image Richardson variety $X^{v^{-1}}_{w^{-1}}$. We say \emph{toric} if corresponding $X_{w^{-1}}^{v^{-1}}$ a toric variety. show when toric, its combinatorial type determined...

We give an explicit description of the Mirkovic-Vilonen cycles on the affine Grassmannian for arbitrary reductive groups. We also give a combinatorial characterization of the MV polytopes. We prove that a polytope is an MV polytope if and only if every 2-face of it is a rank 2 MV polytope.

For a given family of matrices F , we present a methodology to construct (complex) polytope Barabanov norms (and, when F is nonnegative, polytope Barabanov monotone norms and antinorms). Invariant Barabanov norms have been introduced by Barabanov and constitute an important instrument to analyze the joint spectral radius of a set of matrices. In particular, they played a key role in the disprov...

We provide an explicit combinatorial formula for the volume of the polytope of n× n doubly-stochastic matrices, also known as the Birkhoff polytope. We do this through the description of a generating function for all the lattice points of the closely related polytope of n × n real non-negative matrices with all row and column sums equal to an integer t. We can in fact recover similar formulas f...

We extend recent methods for parametric sequence alignment to the parameter space for scoring RNA folds. This involves the construction of an RNA polytope. A vertex of this polytope corresponds to RNA secondary structures with common branching. We use this polytope and its normal fan to study the effect of varying three parameters in the free energy model that are not determined experimentally....