In the last decade, tropical geometry has been attracted a lot of attention in various fields such as the algebraic geometry, computational biology, and physics. The tropical polytope in the tropical geometry was introduced by Develin and Sturmfels as a counterpart of the polytope in the (ordinal) geometry. Recently, in the theory of directed multiflows, it has been shown by Hirai and the autho...

objective: animal studies show that vaccination with epitope-based peptides results in protective immunity. however, immunodominance should be regarded as a major challenge in this area. considering the advantages of epitopic-vaccines against hepatitis c virus (hcv) infection, herein, we compared the occurrence of immunodominance following mice immunization with three different hcv epitopic-pep...

We study the knapsack polytopes that arise whenever the item weights are of two types: either of weight 1 or of weight p. A complete linear description of the associated integral polytope is given by showing that the system is TDI.

1.1. Preamble. Given a graph G = V E and a subset A ⊆ V , the cut determined by A is the vector A ∈ ±1 E with ijth entry −1 if and only if A∩ i j = 1. The cut polytope CUT G is the polytope in E defined as the convex hull of all cuts A (A⊆ V ). Given edge weights w ∈ E , the max-cut problem is the problem of finding a cut A whose weight ∑ ij∈E i∈A j ∈A wij is maximum. Hence, it can be formulate...

Let P be the Gelfand–Tsetlin polytope defined by the skew shape λ/μ and weight w. In the case corresponding to a standard Young tableau, we completely characterize for which shapes λ/μ the polytope P is integral. Furthermore, we show that P is a compressed polytopewhenever it is integral and corresponds to a standard Young tableau.We conjecture that a similar property holds for arbitraryw, name...

The minimum weight feedback vertex set problem (FVS) on series-parallel graphs can be solved in O(n) time by dynamic programming. This solution, however, does not provide a “nice” certificate of optimality. We prove a min-max relation for FVS on series-parallel graphs with no induced subdivision of K2,3 (a class of graphs containing the outerplanar graphs), thereby establishing the existence of...

On the polytope defined in [FFL11], associated to any rectangle highest weight, we define a structure of an type An-crystal. We show, by using the Stembridge axioms, that this crystal is isomorphic to the one obtained from Kashiwara’s crystal bases theory. Further we define on this polytope a bijective map and show that this map satisfies the properties of a weak promotion operator. This implie...

The clique partitioning problem (CPP) can be formulated as follows. Given is a complete graph G = (V; E), with edge weights w ij 2 R for all fi; jg 2 E. A subset A E is called a clique partition if there is a partition of V into non-empty, disjoint sets V 1 S k p=1 ffi; jgji; j 2 V p g. The weight of such a clique partition A is deened as P fi;jg2A w ij. The problem is now to nd a clique partit...