Some Asymptotic Bijections

نویسندگان

  • Edward A. Bender
  • Doron Zeilberger
چکیده

The notion of an asymptotic bijection is introduced and used to give bijective proofs of infinite summation formulas for set partitions (Dobinski's formula) and involutions.

منابع مشابه

The Nature of Partition Bijections Ii. Asymptotic Stability

We introduce a notion of asymptotic stability for bijections between sets of partitions and a class of geometric bijections. We then show that a number of classical partition bijections are geometric and that geometric bijections under certain conditions are asymptotically stable.

متن کامل

More on additive triples of bijections

We study additive properties of the set S of bijections (or permutations) {1, . . . , n} → G, thought of as a subset of Gn, where G is an arbitrary abelian group of order n. Our main result is an asymptotic for the number of solutions to π1 + π2 + π3 = f with π1, π2, π3 ∈ S, where f : {1, . . . , n} → G is an arbitary function satisfying ∑n i=1 f(i) = ∑ G. This extends recent work of Manners, M...

متن کامل

Classification of Bijections between 321- and 132-avoiding Permutations

It is well-known, and was first established by Knuth in 1969, that the number of 321-avoiding permutations is equal to that of 132-avoiding permutations. In the literature one can find many subsequent bijective proofs of this fact. It turns out that some of the published bijections can easily be obtained from others. In this paper we describe all bijections we were able to find in the literatur...

متن کامل

Pattern Avoidance in Labelled Trees

We discuss a new notion of pattern avoidance motivatedby operad theory: pattern avoidance in planar labelled trees. It is a generalisation of various types of consecutive pattern avoidance studied before: consecutive patterns in words, permutations, colouredpermutations, etc. ThenotionofWilf equivalence for patterns in permutations admits a straightforward generalisation for (sets of) tree patt...

متن کامل

Some Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling

In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

متن کامل
عنوان ژورنال:
  • J. Comb. Theory, Ser. A

دوره 38  شماره 

صفحات  -

تاریخ انتشار 1985