We discuss an enumerative technique called generating frees which was introduced in the study of Baxter permutations. We apply the technique to some other classes of permutations with forbidden subsequences. We rederive some known results, e.g. ]S,(132,231)[ = 2” and l&,(123,132,213)1 = F,, and add several new ones: &(123,3241), S,(123,3214),8,(123,2143). Finally, we argue for the broader use o...

We consider the enumeration of multiderangements of a multiset n = {11 , 22 , . . . ,mm} by the number of excedances. We prove several properties, including the invariance under permutations of {n1, n2, . . . , nm}, the symmetry, recurrence relations, the real-rootedness, and a combinatorial expansion, of the generating function dn(x) of multiderangements by excedances, thus generalizing the co...

We introduce two different kind of increasing bilabellings of trees, for which we provide enumeration formulæ. One of the bilabelled tree families considered is enumerated by the reduced tangent numbers and is in bijection with a tree family introduced by Poupard [11]. Both increasing bilabellings naturally lead to hook-length formulas for trees and forests; in particular, one construction give...

We present two classes of random walks restricted to the quarter plane whose generating function is not holonomic. The non-holonomy is established using the iterated kernel method, a recent variant of the kernel method. This adds evidence to a recent conjecture on combinatorial properties of walks with holonomic generating functions. The method also yields an asymptotic expression for the numbe...

A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily identically distributed, nor necessarily all of the same variance. The derivation is based on systematic combinatorial enumeration, study of generating functions, and concentration inequalities of the Poinca...

We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance of the number of (possibly overlapping) ordered labeled subgraphs of a labeled graph as a function of its randomness deficiency (how far it falls short of t...

The Stirling numbers for graphs provide a combinatorial interpretation of the number cycle covers in given graph. problem generating all or enumerating these quantities on general is computationally intractable, but recent work has shown that there exist infinite families sparse structured which it possible to derive efficient enumerative formulas. In this paper, we consider case trees and fore...

Abstract This work is part of an investigation conducted in Italy, which aims to explore the effects instruction on secondary school students’ combinatorial reasoning. We gave a questionnaire adapted from Navarro-Pelayo’s research two groups students with and without combinatorics order analyse performances strategies used their solutions, as well effect same. present results obtained permutati...

We compare the usefulness of the paradigms of radius 1 and radius 1=2 reversible cellular automata. Although the two techniques are equivalent, it is seen that the radius 1=2 paradigm leads to clearer theory, a combinatorial model with good explicit constructions and possibly to a better intuition. The results include related construction methods for both paradigms, in the radius 1=2 case an ex...

We study output-sensitive algorithms and complexity for multiobjective combinatorial optimization problems. In this computational complexity framework, an algorithm for a general enumeration problem is regarded efficient if it is output-sensitive, i.e., its running time is bounded by a polynomial in the input and the output size. We provide both practical examples of MOCO problems for which suc...