相关论文: The enumeration of simple permutations

In the last decade a huge amount of articles has been published studying pattern avoidance on permutations. From the point of view of enumeration, typically one tries to count permutations avoiding certain patterns according to their…

The prefix exchange distance of a permutation is the minimum number of exchanges involving the leftmost element that sorts the permutation. We give new combinatorial proofs of known results on the distribution of the prefix exchange…

Given a prime $p$, we construct a permutation group containing at least $p^{p-2}$ non-conjugated regular elementary abelian subgroups of order $p^3$. This gives the first example of a permutation group with exponentially many non-conjugated…

We construct an injection from the set of permutations of length $n$ that contain exactly one copy of the decreasing pattern of length $k$ to the set of permutations of length $n+2$ that avoid that pattern. We then prove that the generating…

We consider a random permutation drawn from the set of permutations of length $n$ that avoid some given set of patterns of length 3. We show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after suitable…

We introduce the simple extension complexity of a polytope P as the smallest number of facets of any simple (i.e., non-degenerate in the sense of linear programming) polytope which can be projected onto P. We devise a combinatorial method…

A supersequence over a finite set is a sequence that contains as subsequence all permutations of the set. This paper defines an infinite array of methods to create supersequences of decreasing lengths. This yields the shortest known…

The permutation test is known as the exact test procedure in statistics. However, often it is not exact in practice and only an approximate method since only a small fraction of every possible permutation is generated. Even for a small…

Comtet introduced the notion of indecomposable permutations in 1972. A permutation is indecomposable if and only if it has no proper prefix which is itself a permutation. Indecomposable permutations were studied in the literature in various…

In this paper, we find an explicit formula for the generating function that counts the circular permutations of length n avoiding the pattern 23 4 1 whose enumeration was raised as an open problem by Rupert Li. This then completes in all…

We prove several results regarding the simplicity of germs and multigerms obtained via the operations of augmentation, simultaneous augmentation and concatenation and generalised concatenation. We also give some results in the case where…

A permutiple is a natural number that is a nontrivial multiple of a permutation of its digits in some base. Special cases of permutiples include cyclic numbers (multiples of cyclic permutations of their digits) and palintiple numbers…

In this paper, we introduce a new method for computing generating functions with respect to the number of descents and left-to-right minima over the set of permutations which have no consecutive occurrences of a pattern that starts with 1.

A simple linear loop is a simple while loop with linear assignments and linear loop guards. If a simple linear loop has only two program variables, we give a complete algorithm for computing the set of all the inputs on which the loop does…

It is well-known that any permutation can be written as a product of two involutions. We provide an explicit formula for the number of ways to do so, depending only on the cycle type of the permutation. In many cases, these numbers are sums…

We discuss permutation representations which are obtained by the natural action of $S_n \times S_n$ on some special sets of invertible matrices, defined by simple combinatorial attributes. We decompose these representations into…

Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…

A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and…

In this paper we use a probabilistic approach to derive the expressions for the characteristic functions of basic statistics defined on permutation tableaux. Since our expressions are exact, we can identify the distributions of basic…

Universal cycle for $k$-permutations is a cyclic arrangement in which each $k$-permutation appears exactly once as $k$ consecutive elements. Enumeration problem of universal cycles for $k$-permutations is discussed and one new enumerating…