A new systematic approach for the speciication of bijections between sets of combinatorial objects is presented. It is based on the notion of object grammars. Object grammmars are recursive descriptions of objects which generalize context free grammars. The study of a particular substitution in these object grammars connrms once more the key role of Dyck words in the domain of enumerative and b...

The material gives a new combinatorial proof of the multiplicative property of the S-transform. In particular, several properties of the coefficients of its inverse are connected to non-crossing linked partitions and planar trees. AMS subject classification: 05A10 (Enumerative Combinatorics); 46L54(Free Probability and Free Operator Algebras).

The. theory of reduced incidence algebras of binomial posets furnishes a unified treatment of several types of generating functions that arise in enumerative combinatorics. Using this theory as a tool, we study ‘reduced covering algebras’ of binomial lattices and show that they are isomorphic to various algebras of q-binomial generating functions for certain modular binomial lattices.

This is a review (including some background material) of the author’s work and related activity on certain exactly solvable statistical models in two dimensions, including the six-vertex model, loop models and lozenge tilings. Applications to enumerative combinatorics and to algebraic geometry are described.

This work establishes a connection between gravitational quantum cohomology and enumerative geometry of rational curves (in a projective homogeneous variety) subject to conditions of infinitesimal nature like, for example, tangency. The key concept is that of modified psi classes, which are well suited for enumerative purposes and substitute the tautological psi classes of 2D gravity. The main ...

Generalizing a classical problem in enumerative combinatorics, Mansour and Sun counted the number of subsets of Zn without certain separations. Chen, Wang, and Zhang then studied the problem of partitioning Zn into arithmetical progressions of a given type under some technical conditions. In this paper, we improve on their main theorems by applying a convolution formula for cyclic multinomial c...

In this short article I introduce the multipol package, which provides some functionality for handling multivariate polynomials; the package is discussed here from a programming perspective. An example from the field of enumerative combinatorics is presented. This vignette is based on Hankin (2008).

When first introduced to the analysis of algorithms, students are taught how to assess the best and worst cases, whereas the mean and amortized costs are considered advanced topics, usually saved for graduates. When presenting the latter, aggregate analysis is explained first because it is the most intuitive kind of amortized analysis, often involving enumerative combinatorics. We show how the ...

Based on Schützenberger’s evacuation and a modification of jeu de taquin, we give a bijective proof of an identity connecting the generating function of reverse semistandard Young tableaux with bounded entries with the generating function of all semistandard Young tableaux. This solves Exercise 7.102 b of Richard Stanley’s book ‘Enumerative Combinatorics 2’.

The study of pattern containment and avoidance for linear permutations is a well-established area enumerative combinatorics. A cyclic permutation the set all rotations permutation. Vella Callan independently initiated in characterized classes single length 4. We continue this work. In particular, we derive results about multiple patterns 4, determine generating functions descent statistic on th...