Related papers: Pattern avoidance with involution

An alternating permutation of length $n$ is a permutation $\pi=\pi_1 \pi_2 ... \pi_n$ such that $\pi_1 < \pi_2 > \pi_3 < \pi_4 > ...$. Let $A_n$ denote set of alternating permutations of ${1,2,..., n}$, and let $A_n(\sigma)$ be set of…

We prove the so-called Unitary Isotropy Theorem, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic involutions as well as on hyperbolicity of orthogonal,…

This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a…

In this article, we propose a concept of anti-involution for Green biset functors and we provide equivalent definitions. We present $\star$-Green biset functors and we study their orthogonal units and the orthogonal automorphisms in their…

In this work we approach three-dimensional evolution algebras from certain constructions performed on two-dimensional algebras. More precisely, we provide four different constructions producing three-dimensional evolution algebras from…

We characterize universally generalizing morphisms which satisfy descent of algebraic cycles integrally as those universally generalizing morphisms which are surjective with generically reduced fibres. In doing so, we introduce a naive…

Iterative projection methods may become trapped at non-solutions when the constraint sets are nonconvex. Two kinds of parameters are available to help avoid this behavior and this study gives examples of both. The first kind of parameter,…

We consider the inverse scattering problem associated with any number of interacting modes in one-dimensional structures. The coupling between the modes is contradirectional in addition to codirectional, and may be distributed continuously…

We present some combinatorial interpretations for coefficients appearing in series partitioning the permutations avoiding 132 along marked mesh patterns. We identify for patterns in which only one parameter is non zero the combinatorial…

In this paper, the problem of pattern avoidance in generalized non-crossing trees is studied. The generating functions for generalized non-crossing trees avoiding patterns of length one and two are obtained. Lagrange inversion formula is…

This short paper is concerned with the enumeration of permutations avoiding the following four patterns: $2431$, $4231$, $1432$ and $4132$. Using a bijective construction, we prove that these permutations are counted by the central binomial…

Let $\pi$ be a cyclic permutation that can be expressed in its one-line form as $\pi = \pi_1\pi_2 \cdot\cdot\cdot \pi_n$ and in its standard cycle form as $\pi = (c_1,c_2, ..., c_n)$ where $c_1=1$. Archer et al. introduced the notion of…

We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…

Hultman, Linusson, Shareshian, and Sj\"ostrand gave a pattern avoidance characterization of the permutations for which the number of chambers of its associated inversion arrangement is the same as the size of its lower interval in Bruhat…

We consider an isomorphism invariant for measure-preserving systems - types of generalized entropy convergence rates. We show the connections of this invariant with the types of Shannon entropy convergence rates. In the case when they…

We present identities for permutations with fixed points. The formulas are based on successive derivations or integrations of the determinant of a particular matrix.

We present a deterministic comparison-based algorithm that sorts sequences avoiding a fixed permutation $\pi$ in linear time, even if $\pi$ is a priori unkown. Moreover, the dependence of the multiplicative constant on the pattern $\pi$…

Changing base composition during the evolution of biological sequences can mislead some of the phylogenetic inference techniques in current use. However, detecting whether such a process has occurred may be difficult, since convergent…

We prove that all injective maps on positive complex matrices which preserve order and shrink spectrum are implemented by unitary or antiunitary conjugations. We show by counterexamples that all assumptions are indispensable. The result…

If two G-manifolds are G-cobordant then characteristic numbers corresponding to the fixed point sets (submanifolds) of subgroups of G and to normal bundles to these sets coincide. We construct two analogues of these characteristic numbers…