JCT
2007
13 years 4 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 4 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 4 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 4 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 4 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 4 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 4 months ago
2007
JCT
2007
13 years 4 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 4 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 4 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...