Name
Abstract | ||
|---|---|---|
Martin Klazar computed the total weight of ordered trees under 12 different notions of weight. The last and perhaps the most interesting of these weights, w"1"2, led to a recurrence relation and an identity for which he requested combinatorial explanations. Here we provide such explanations. To do so, we introduce the notion of a ''Klazar violator'' vertex in an increasing ordered tree and observe that w"1"2 counts what we call Klazar trees-increasing ordered trees with no Klazar violators. A highlight of the paper is a bijection from n-edge increasing ordered trees to perfect matchings of [2n]={1,2,...,2n} that sends Klazar violators to even numbers matched to a larger odd number. We find the distribution of the latter matches and, in particular, establish the one-summation explicit formula @?"k"="1^@?^n^/^2^@?(2k-1)!!^2{n+12k+1} for the number of perfect matchings of [2n] with no even-to-larger-odd matches. The proofs are mostly bijective. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.ejc.2009.11.004 | Eur. J. Comb. |
Keywords | Field | DocType |
one-summation explicit formula,different notion,combinatorial explanation,perfect matchings,latter match,larger odd number,martin klazar,total weight,klazar trees-increasing,klazar violator,recurrence relation | Discrete mathematics,Combinatorics,Bijection,Vertex (geometry),Recurrence relation,Mathematical proof,Parity (mathematics),Mathematics | Journal |
Volume | Issue | ISSN |
31 | 5 | 0195-6698 |
Citations | PageRank | References |
1 | 0.48 | 3 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| David Callan | 1 | 7 | 5.50 |