On the Exhaustive Generation of Plane Partitions

We present a CAT (Constant Amortized Time) algorithm for generating all plane partitions of an integer n, that is, all integer matrices with non-increasing rows and columns having sum n

Random and exhaustive generation of permutations and cycles

In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. This algorithm is very similar to the standard method for generating a random permutation, but is less well known. We consider both methods in a unified way, and discuss their relation with exhaustive generation methods. We analyse several random variables associated with the algorithms and find their grand probability generating functions, which gives easy access to moments and limit laws.Comment: 9 page

Coloured peak algebras and Hopf algebras

For $G$ a finite abelian group, we study the properties of general equivalence relations on G_n=G^n\rtimes \SG_n, the wreath product of $G$ with the symmetric group \SG_n, also known as the $G$-coloured symmetric group. We show that under certain conditions, some equivalence relations give rise to subalgebras of \k G_n as well as graded connected Hopf subalgebras of \bigoplus_{n\ge o} \k G_n. In particular we construct a $G$-coloured peak subalgebra of the Mantaci-Reutenauer algebra (or $G$-coloured descent algebra). We show that the direct sum of the $G$-coloured peak algebras is a Hopf algebra. We also have similar results for a $G$-colouring of the Loday-Ronco Hopf algebras of planar binary trees. For many of the equivalence relations under study, we obtain a functor from the category of finite abelian groups to the category of graded connected Hopf algebras. We end our investigation by describing a Hopf endomorphism of the $G$-coloured descent Hopf algebra whose image is the $G$-coloured peak Hopf algebra. We outline a theory of combinatorial $G$-coloured Hopf algebra for which the $G$-coloured quasi-symmetric Hopf algebra and the graded dual to the $G$-coloured peak Hopf algebra are central objects.Comment: 26 pages latex2

Balance Properties and Distribution of Squares in Circular Words

We study balance properties of circular words over alphabets of size greater than two. We give some new characterizations of balanced words connected to the Kawasaki-Ising model and to the notion of derivative of a word. Moreover we consider two different generalizations of the notion of balance, and we find some relations between them. Some of our results can be generalised to non periodic infinite words as well

Balance Properties and Distribution of Squares in Circular Words

We study balance properties of circular words over alphabets of size greater than two. We give some new characterizations of balanced words connected to the Kawasaki-Ising model and to the notion of derivative of a word. Moreover we consider two different generalizations of the notion of balance, and we find some relations between them. Some of our results can be generalized to non periodic infinite words as well

An efficient algorithm for generating symmetric ice piles

International audienc

On the generation of 2-polyominoes

The class of 2-polyominoes contains all polyominoes P such that for any integer i, the first i columns of P consist of at most 2 polyominoes. We provide a decomposition that allows us to exploit suitable discrete dynamical systems to define an algorithm for generating all 2-polyominoes of area n in constant amortized time and space O(n)

Lightweight Metagenomic Classification via eBWT

The development of Next Generation Sequencing has had a major impact on the study of genetic sequences, and in particular, on the advancement of metagenomics, whose aim is to identify the microorganisms that are present in a sample collected directly from the environment. In this paper, we describe a new lightweight alignment-free and assembly-free framework for metagenomic classification that compares each unknown sequence in the sample to a collection of known genomes. We take advantage of the combinatorial properties of an extension of the Burrows-Wheeler transform, and we sequentially scan the required data structures, so that we can analyze unknown sequences of large collections using little internal memory. For the best of our knowledge, this is the first approach that is assembly- and alignment-free, and is not based on k-mers. We show that our experiments confirm the effectiveness of our approach and the high accuracy even in negative control samples. Indeed we only classify 1 short read on 5,726,358 random shuffle reads. Finally, the results are comparable with those achieved by read-mapping classifiers and by k-mer based classifiers