JCT
2010
13 years 3 months ago
2010
The concept of intersection numbers of order r for t-designs is generalized to graphs and to block designs which are not necessarily t-designs. These intersection numbers satisfy ...
JCT
2010
13 years 3 months ago
2010
JCT
2010
13 years 3 months ago
2010
The pattern-avoiding fillings of Young diagrams we study arose from Postnikov’s work on positive Grassman cells. They are called Γ -diagrams, and are in bijection with decorate...
JCT
2010
13 years 3 months ago
2010
We present a partial generalization to Schubert calculus on flag varieties of the classical Littlewood-Richardson rule, in its version based on Sch¨utzenberger’s jeu de taquin....
JCT
2010
13 years 3 months ago
2010
We prove a vector space analog of a version of the Kruskal-Katona theorem due to Lov´asz. We apply this result to extend Frankl’s theorem on r-wise intersecting families to vec...
JCT
2010
13 years 3 months ago
2010
Let m1, m2, . . . , mt be a list of integers. It is shown that there exists an integer N such that for all n ≥ N, the complete graph of order n can be decomposed into edge-disjo...
JCT
2010
13 years 3 months ago
2010
JCT
2010
13 years 3 months ago
2010
Abstract. We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2 + 2)-free posets and a certain class of involutions (or chord ...
JCT
2010
13 years 3 months ago
2010
Combinatorial proofs are given for certain entries in Ramanujan’s lost notebook. Bijections of Sylvester, Franklin, Wright, and Yee are employed. A new bijection, involving the n...
JCT
2010
13 years 3 months ago
2010
We propose a major index statistic on 01-fillings of moon polyominoes which, when specialized to certain shapes, reduces to the major index for permutations and set partitions. W...