Abstract We determine the asymptotics of number independent sets size $\lfloor \beta 2^{d-1} \rfloor$ in discrete hypercube $Q_d = \{0,1\}^d$ for any fixed $\beta \in (0,1)$ as $d \to \infty$ , extending a result Galvin (1-1/\sqrt{2},1)$ . Moreover, we prove multivariate local central limit theorem structural features $Q_d$ drawn according to hard-core model at fugacity $\lambda>0$ In provin...

The study of parity-alternating permutations of {1, 2, . . . , n} is extended to permutations containing a prescribed number of parity successions – adjacent pairs of elements of the same parity. Several enumeration formulae are computed for permutations containing a given number of parity successions, in conjunction with further parity and length restrictions. The objects are classified using ...

We present a fast enumeration algorithm for combinatorial 2and 3-manifolds. In particular, we enumerate all triangulated surfaces with 11 and 12 vertices and all triangulated 3-manifolds with 11 vertices. We further determine all equivelar maps on the non-orientable surface of genus 4 as well as all equivelar triangulations of the orientable surface of genus 3 and the non-orientable surfaces of...

The problem of constructing quasi equidistant and reflected binary Gray code sequences and code in a mixed factorial, Fibonacci and binomial numeration systems is considered in the article. Some combinatorial constructions and machine algorithms synthesis sequences, based on the method of directed enumeration are offered. For selected parameters of sequences all quasi equidistant (for individua...

We present new, simple proofs for the enumeration of five of the ten symmetry classes of plane partitions contained in a given box. Four of them are derived from a simple determinant evaluation, using combinatorial arguments. The previous proofs of these four cases were quite complicated. For one more symmetry class we give an elementary proof in the case when two of the sides of the box are eq...

We give an extension of the famous Schensted correspondence to the case of ribbon tableaux, where ribbons are allowed to be of different sizes. This is done by extending Fomin’s growth diagram approach of the classical correspondence, in particular by allowing signs in the enumeration. As an application, we give in particular a combinatorial proof, based on the Murnaghan–Nakayama rule, for the ...

A recent progress on the complete enumeration of oriented matroids enables us to generate all combinatorial types of small point configurations and hyperplane arrangements in general dimension, including degenerate ones. This extends a number of former works which concentrated on the non-degenerate case and are usually limited to dimension 2 or 3. Our initial study on the complete list for smal...

In this paper we present a method to pass from a recurrence relation having constant coefficients (in short, a C-recurrence) to a finite succession rule defining the same number sequence. We recall that succession rules are a recently studied tool for the enumeration of combinatorial objects related to the ECO method. We also discuss the applicability of our method as a test for the positivity ...

The generating functions for a large class of combinatorial problems involving the enumeration of permutations may be expressed as solutions to matrix Riccati equations. We show that the generating functions for the permutation problem in which the number of inversions is also preserved form a system of matrix Riccati equations in which the differential operator is the Eulerian differential ope...

ECO is a method for the enumeration of classes of combinatorial objects based on recursive constructions of such classes. In the first part of this paper we present a construction for the class of convex polyominoes based on the ECO method. Then we translate this construction into a succession rule. The final goal of the paper is to determine the generating function of convex polyominoes accord...