相关论文: On the X-rays of permutations
A review is given on aspects of indirect imaging techniques in X-ray binaries which are used as diagnostics tools for probing the X-ray dominated accretion disc physics. These techniques utilize observed properties such as the emission line…
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 introduce ballot matrices, a signed combinatorial structure whose definition naturally follows from the generating function for labeled interval orders. A sign reversing involution on ballot matrices is defined. We show that matrices…
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
The A-hierarchy is a parametric analogue of the polynomial hierarchy in the context of paramterised complexity theory. We give a new characterisation of the A-hierarchy in terms of a generalisation of the SUBSET-SUM problem.
Using the diagrammatic approach to integrals over Gaussian random matrices, we find a representation for polynomial Lie group integrals as infinite sums over certain maps on surfaces. The maps involved satisfy a specific condition: they…
This paper introduces a polynomial blind algorithm that determines when two square matrices, $A$ and $B$, are permutation similar. The shifted and translated matrices $(A+\beta I+\gamma J)$ and $(B+\beta I+\gamma J)$ are used to color the…
Baxter permutations are known to be in bijection with a wide number of combinatorial objects. Previously, it was shown that each of these objects had a natural involution which was carried equivariantly by the known bijections, and the…
The success of machine learning algorithms is inherently related to the extraction of meaningful features, as they play a pivotal role in the performance of these algorithms. Central to this challenge is the quality of data representation.…
Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be…
We consider the problem of factoring permutations as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances. In particular, we investigate the minimum number, $\delta$, such…
Following the footprints of what have been done with the algorithm Stacksort, we investigate the preimages of the map associated with a slightly less well known algorithm, called Queuesort. After having described an equivalent version of…
We consider the relation between various permutation statistics and properties of permutation tableaux. We answer some of the questions of Steingrimsson and Williams (math.CO/0507149), in particular, on the distribution of the bistatistic…
We study sums of the form $\sum_{k=m}^n a_{nk} b_{km}$, where $a_{nk}$ and $b_{km}$ are binomial coefficients or unsigned Stirling numbers. In a few cases they can be written in closed form. Failing that, the sums still share many common…
Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a metaphoric sense in which a rope is made from a bundle of…
We present new models for illuminated accretion disks, their structure and reprocessed emission. We consider the effects of incident X-rays on the surface of an accretion disk by solving simultaneously the equations of radiative transfer,…
The $n$-th rencontres number with the parameter $r$ is the number of permutations having exactly $r$ fixed points. In particular, a derangement is a permutation without any fixed point. We presents a short combinatorial proof for a weighted…
The representation theory of a commutative noetherian ring is tightly controlled by its prime spectrum. In this article we use the prime spectrum to describe mutation of cosilting objects in the derived category of a commutative noetherian…
This paper introduces two matrix analogues for set partitions. A composition matrix on a finite set X is an upper triangular matrix whose entries partition X, and for which there are no rows or columns containing only empty sets. A…
Permutations can be represented as linear combinations of natural numbers with different powers. In this paper, its coefficient matrix and inverse matrix is derived, and the results show the coefficient matrix is a lower triangular matrix…