Related papers: A code for square permutations and convex permutom…
We establish a novel bijective encoding that represents permutations as forests of decorated (or enriched) trees. This allows us to prove local convergence of uniform random permutations from substitution-closed classes satisfying a…
Natural numbers which are nontrivial multiples of some permutation of their base-$b$ digit representations are called permutiples. Specific cases include numbers which are multiples of cyclic permutations (cyclic numbers) and reversals of…
An M-sequence generated by a primitive polynomial has many interesting and desirable properties. A pseudo-random array is the two-dimensional generalization of an M-sequence. There are non-primitive polynomials all of whose non-zero…
Characterizing sets of permutations whose associated quasisymmetric function is symmetric and Schur-positive is a long-standing problem in algebraic combinatorics. In this paper we present a general method to construct Schur-positive sets…
Permutation polynomials over finite fields have important applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, etc. In this paper, we construct several new classes of permutation…
In this paper convolutional codes with cyclic structure will be investigated. These codes can be understood as left principal ideals in a suitable skew-polynomial ring. It has been shown in [3] that only certain combinations of the…
We explore how the asymptotic structure of a random permutation of $[n]$ with $m$ inversions evolves, as $m$ increases, establishing thresholds for the appearance and disappearance of any classical, consecutive or vincular pattern. The…
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…
A square is a factor $S = (S_1; S_2)$ where $S_1$ and $S_2$ have the same pattern, and a permutation is said to be square-free if it contains no non-trivial squares. The permutation is further said to be bicrucial if every extension to the…
An infinite permutation is a linear order on the set N. We study the properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.
A systematic procedure is developed for constructing fermion systems in discrete space-time which have a given outer symmetry. The construction is illustrated by simple examples. For the symmetric group, we derive constraints for the number…
A sweep of a point configuration is any ordered partition induced by a linear functional. Posets of sweeps of planar point configurations were formalized and abstracted by Goodman and Pollack under the theory of allowable sequences of…
We study sorting by queues that can rearrange their content by applying permutations from a predefined set. These new sorting devices are called shuffle queues and we investigate those of them corresponding to sets of permutations defining…
Let ${\mathcal P}\subset{\mathbb Z}^2$ be a convex polygon with each vertex in it labeled by an element from a finite set and such that the labeling of each vertex $v\in {\mathcal P}$ is uniquely determined by the labeling of all other…
The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework.…
In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum…
We study the lattice of submonoids of the uniform block permutation monoid containing the symmetric group (which is its group of units). We prove that this lattice is distributive under union and intersection by relating the submonoids…
A sample of n generic points in the xy-plane defines a permutation that relates their ranks along the two axes. Every subset of k points similarly defines a pattern, which occurs in that permutation. The number of occurrences of small…
This paper presents an algorithmic method for generating random orthogonal matrices \(A\) that satisfy the property \(A^t S A = S\), where \(S\) is a fixed real invertible symmetric or skew-symmetric matrix. This method is significant as it…
A deflatable permutation class is one in which the simple permutations are contained in a proper subclass. Deflatable permutation classes are often easier to describe and enumerate than non-deflatable ones. Some theorems which guarantee…