JCT
2010
13 years 10 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 10 months ago
2010
JCT
2010
13 years 10 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 10 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 10 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 10 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 10 months ago
2010
JCT
2010
13 years 10 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 10 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 10 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...