Related papers: Diagrams and essential sets for signed permutation…
This article studies the poset of simple permutations with respect to the pattern involvement. We specify results on critically indecomposable posets obtained by Schmerl and Trotter to simple permutations and prove that if $\sigma, \pi$ are…
In this paper, we start by giving the definitions and basic facts about hyperoctahedral number system. There is a natural correspondence between the integers expressed in the latter and the elements of the hyperoctahedral group when we use…
Theta-vexillary signed permutations are elements in the hyperoctahedral group that index certain classes of degeneracy loci of type B and C. These permutations are described using triples of $s$-tuples of integers subject to specific…
Many important statistics of signed permutations are realized in the corresponding permutation tableaux or bare tableaux of type $B$: Alignments, crossings and inversions of signed permutations are realized in the corresponding permutation…
Stanley introduced in 1986 the order polytope and the chain polytope for a given finite poset. These polytopes contain much information about the poset and have given rise to important examples in polyhedral geometry. In 1993, Reiner…
The periodic (ordinal) patterns of a map are the permutations realized by the relative order of the points in its periodic orbits. We give a combinatorial characterization of the periodic patterns of an arbitrary signed shift, in terms of…
Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed…
In this paper, we present an algorithm that enumerates a certain class of signed permutations, referred to as grid signed permutation classes. In the case of permutations, the corresponding grid classes are of interest because they are…
Let $s$ be West's deterministic stack-sorting map. A well-known result (West) is that any length $n$ permutation can be sorted with $n-1$ iterations of $s.$ In 2020, Defant introduced the notion of highly-sorted permutations -- permutations…
We study the combinatorial properties of vexillary signed permutations, which are signed analogues of the vexillary permutations first considered by Lascoux and Sch\"utzenberger. We give several equivalent characterizations of vexillary…
We extend the short presentation due to [Borel '53] of the cohomology ring of a generalized flag manifold to a relatively short presentation of the cohomology of any of its Schubert varieties. Our result is stated in a root-system uniform…
We study the combinatorial equivalence of separable elements in types $A$ and $B$. A bijection is constructed from the set of separable permutations in the symmetric group $S_{n+1}$ to the set of separable signed permutations in the…
We prove the existence of signed combinatorial interpretations for several large families of structure constants. These families include standard bases of symmetric and quasisymmetric polynomials, as well as various bases in Schubert…
Motivation coming from the study of affine Weyl groups, a structure of ranked poset is defined on the set of circular permutations in $S_n$ (that is, $n$-cycles). It is isomorphic to the poset of so-called admitted vectors, and to an…
Signed shifts are generalizations of the shift map in which, interpreted as a map from the unit interval to itself sending x to the fractional part of Nx, some slopes are allowed to be negative. Permutations realized by the relative order…
By introducing the notion of relative derangements of type $B$, also called signed relative derangements, which are defined in terms of signed permutations, we obtain a type $B$ analogue of the well-known relation between relative…
Permutation modules play an important role in the representation theory of the symmetric group. Hartmann and Paget defined permutation modules for non-degenerate Brauer algebras. We generalise their construction to a wider class of…
Pinnacle sets record the values of the local maxima for a given family of permutations. They were introduced by Davis-Nelson-Petersen-Tenner as a dual concept to that of peaks, previously defined by Billey-Burdzy-Sagan. In recent years…
For a graph with edge ordering, a linear order on the edge set, we obtain a permutation of vertices by considering the edges as transpositions of endvertices. It is known from D\'enes' results that the permutation of a tree is a full cyclic…
The W-set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. We explicitly describe in a purely combinatorial manner the W-sets of the weak order…