منابع مشابه
On the mean radius of permutation polytopes
Let X S n be a subset of the symmetric group S n and let Q X IR n 2 be the convex hull of the set of permutation matrices representing the elements of X in IR n 2. We present some formulas relating the cardinality of X and the maximal value of a typical linear function on Q X. Applications to the average case analysis of Combinatorial Optimization problems and to eecient counting are discussed.
متن کاملOn Permutation Polytopes - Notions of Equivalence
By assigning a permutation polytope to a group we produce new interesting polytopes. For the effective use of this construction method it is desirable to understand which groups are leading to affine equivalent polytopes. Therefore, the notion of effective equivalence has been introduced [BHNP09]. In this note we clarify the notion of effective equivalence and characterize geometrically the eff...
متن کاملPermutation Polytopes of Cyclic Groups
We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. In the situation that the generator of the group consists of at most two orbits, we can give a complete combinatorial description of the associated permutation polytope. In the case of three orbits the facet structure is...
متن کاملPermutation polytopes and indecomposable elements in permutation groups
Each group G of n × n permutation matrices has a corresponding permutation polytope, P (G) := conv(G) ⊂ R. We relate the structure of P (G) to the transitivity of G. In particular, we show that if G has t nontrivial orbits, then min{2t, ⌊n/2⌋} is a sharp upper bound on the diameter of the graph of P (G). We also show that P (G) achieves its maximal dimension of (n − 1) precisely when G is 2-tra...
متن کاملGeometry, Complexity, and Combinatorics of Permutation Polytopes
Each group G of permutation matrices gives rise to a permutation polytope P(G) = cony(G) c Re×d, and for any x ~ W, an orbit polytope P(G, x) = conv(G, x). A broad subclass is formed by the Young permutation polytopes, which correspond bijectively to partitions 2 = (21, ..., 2k)~-n of positive integers, and arise from the Young representations of the symmetric group. Young polytopes provide a f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2009
ISSN: 0001-8708
DOI: 10.1016/j.aim.2009.05.003