Let Sn and Bn denote the respective sets of ordinary and bigrassmannian permutations of order n, and let (Sn,≤) denote the Bruhat ordering permutation poset. We extensively study the structural properties of the restricted poset (Bn,≤), showing among other things that it is ranked, symmetric, and possesses the Sperner property. We also give formulae for the number of bigrassmannian permutations...

Jens Gustedt, Michel Morvan, Laurent Viennot. A compact data structure and parallel algorithms for permutation graphs. M. Nagl. 21st Workshop on Graph-Theoretic Concepts in computer Science (WG), 1995, Aachen, Germany. Springer Berlin / Heidelberg, 1017, pp.372380, 1995, Lecture Notes in Computer Science; Graph-Theoretic Concepts in Computer Science. <http://www.springerlink.com/content/f161001...

Statistical parametric mapping (SPM) analysis of fMRI data requires specifying correctly the temporal and spatial noise covariance structure. This is a difficult if not impossible task. When these assumptions are not satisfied, statistical inference can be invalid or inefficient. Permutation tests are free of strong assumptions on the distribution of signal noise. We propose permutation tests o...

A permutation graph is an intersection graph of segments lying between two parallel lines. A Seidel complementation of a finite graph at a vertex v consists in complementing the edges between the neighborhood and the non-neighborhood of v. Two graphs are Seidel complement equivalent if one can be obtained from the other by a sequence of Seidel complementations. In this paper we introduce the ne...

We study the facial structure of two important permutation polytopes in R n 2 , the Birkho or assignment polytope B n , de ned as the convex hull of all n n permutation matrices, and the asymmetric traveling salesman polytope T n , de ned as the convex hull of those n n permutation matrices corresponding to n-cycles. Using an isomorphism between the face lattice of B n and the lattice of elemen...

The Polya cycle index has been a key tool in understanding what a typical permutation π ∈ Sn ”looks like”. It is useful for studying properties of a permutation which depend only on its cycle structure. Here are some examples of theorems which can be proved using the cycle index. Lloyd and Shepp [25] showed that for any i < ∞, the joint distribution of (a1(π), · · · , ai(π)) for π chosen unifor...

Circular permutation describes a type of relationship between proteins, whereby the proteins have a changed order of amino acids in their protein sequence, such that the sequence of the first portion of one protein (adjacent to the N-terminus) is related to that of the second portion of the other protein (near its C-terminus), and vice versa (see Figure 1). This is directly analogous to the mat...

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...