相关论文: Automatic enumeration of regular objects

Biclustering has proved to be a powerful data analysis technique due to its wide success in various application domains. However, the existing literature presents efficient solutions only for enumerating maximal biclusters with constant…

We present the first combinatorial scheme for counting labelled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function of labelled 4-regular planar graphs can be…

Let $G$ be a finite group generated by $k$ elements. The well-known product replacement algorithm provides an effective method for sampling generating sets of $G$. We study a refinement of this algorithm that is designed to output…

Nominal sets provide a foundation for reasoning about names. They are used primarily in syntax with binders, but also, e.g., to model automata over infinite alphabets. In this paper, nominal sets are related to nominal renaming sets, which…

We describe arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects specified as a Haskell type class. Our algorithms work on a {\em generic} representation that we illustrate on…

Integer partitions are one of the most fundamental objects of combinatorics (and number theory), and so is enumerating objects avoiding patterns. In the present paper we describe two approaches for the systematic counting of classes of…

Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…

Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…

This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…

In this paper we use the framework of automatic sequences to study combinatorial sequences modulo prime powers. Given a sequence whose generating function is the diagonal of a rational power series, we provide a method, based on work of…

A method for selecting solution constructors in narrowing is presented. The method is based on a sort discipline that describes regular sets of ground constructor terms as sorts. It is extended to cope with regular sets of ground…

We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups of automatic groups which are not even…

We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the…

We study enumeration functions for unimodal sequences of positive integers, where the size of a sequence is the sum of its terms. We survey known results for a number of natural variants of unimodal sequences, including Auluck's generalized…

This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include…

This paper summarizes our latest understanding and results about the application of the Mathematics Of Enumeration to Tanner Graphs that have a regular structure called Balanced Tanner Graphs. Some preliminaries of permutation groups have…

We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding…

For enumerative problems, i.e. computable functions f from N to Z, we define the notion of an effective (or closed) formula. It is an algorithm computing f(n) in the number of steps that is polynomial in the combined size of the input n and…

This contribution summarizes recent work of the authors that combines methods from dynamical systems theory (discrete Painlev\'e equations) and asymptotic analysis of orthogonal polynomial recurrences, to address long-standing questions in…

Guo-Niu Han [arXiv:2006.14070 [math.CO]] has introduced a new combinatorial object named standard puzzle. We use digraphs to show the relations between numbers in standard puzzles and propose a skeleton model. By this model, we solve the…