JCT
2007
13 years 11 months ago
2007
We characterise the permutations π such that the elements in the closed lower Bruhat interval [id,π] of the symmetric group correspond to non-taking rook configurations on a sk...
JCT
2007
13 years 11 months ago
2007
Abstract. Simple families of increasing trees can be constructed from simply generated tree families, if one considers for every tree of size n all its increasing labellings, i.e.,...
JCT
2007
13 years 11 months ago
2007
In two previous papers, the study of partitions with short sequences has been developed both for its intrinsic interest and for a variety of applications. The object of this paper...
JCT
2007
13 years 11 months ago
2007
Given a sequence of integers b = (b0,b1,b2,...) one gives a Dyck path P of length 2n the weight wt(P) = bh1 bh2 ···bhn , where hi is the height of the ith ascent of P. The corr...
JCT
2007
13 years 11 months ago
2007
For an r-graph H, let C(H) = minS d(S), where the minimum is taken over all (r − 1)-sets of vertices of H, and d(S) is the number of vertices v such that S ∪ {v} is an edge of...
JCT
2007
13 years 11 months ago
2007
Abstract. Let n and k be natural numbers and let S(n, k) denote the Stirling numbers of the second kind. It is a conjecture of Wilf that the alternating sum nX j=0 (−1)j S(n, j) ...
JCT
2007
13 years 11 months ago
2007
JCT
2007
13 years 11 months ago
2007
Abstract. We consider lattice walks in the plane starting at the origin, remaining in the first quadrant i, j ≥ 0 and made of West, South and North-East steps. In 1965, Germain ...
JCT
2007
13 years 11 months ago
2007
We describe a general construction principle for a class of self-similar graphs. For various enumeration problems, we show that this construction leads to polynomial systems of rec...
JCT
2007
13 years 11 months ago
2007
We define a q generalization of weighted Catalan numbers studied by Postnikov and Sagan, and prove a result on the divisibility by p of such numbers when p is a prime and q its p...