Garsia and Milne's bijective proof of the inclusion-exclusion principle

نویسنده

  • Doron Zeilberger
چکیده

Although the following proof is implicit in Garsia and Milne's paper [I], it is scj elegant that we felt that it should be presented by itself for the benefit of the general mathematical public. The idea behind the proof was further exploited by Remmel [2] and Wilf [3]. Consider a set A of elements each of which possess a (possibly emptyj subset of the properties (1,. .. , n}. The inclusion-exclusion principle states that the number of elements with no properties is

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Kernel operators and improved inclusion-exclusion bounds

We present a new and elementary proof of some recent improvements of the classical inclusion-exclusion bounds. The key idea is to use an injective mapping, similar to the bijective mapping in Garsia and Milne’s “bijective” proof of the classical inclusion-exclusion principle.

متن کامل

Another Involution Principle-Free Bijective Proof of Stanley's Hook-Content Formula

Another bijective proof of Stanley’s hook-content formula for the generating function for semistandard tableaux of a given shape is given that does not involve the involution principle of Garsia and Milne. It is the result of a merge of the modified jeu de taquin idea from the author’s previous bijective proof (“An involution principle-free bijective proof of Stanley’s hook-content formula”, Di...

متن کامل

A Bijective Proof of a Major Index Theorem of Garsia and Gessel

In this paper we provide a bijective proof of a theorem of Garsia and Gessel describing the generating function of the major index over the set of all permutations of [n] = {1, ..., n} which are shuffles of given disjoint ordered sequences π1, ..., πk whose union is [n]. The proof is based on a result (an “insertion lemma”) of Haglund, Loehr, and Remmel which describes the change in major index...

متن کامل

Bijective proofs of the hook formulas for the number of standard Young tableaux, ordinary and shifted

Bijective proofs of the hook formulas for the number of ordinary standard Young tableaux and for the number of shifted standard Young tableaux are given. They are formulated in a uniform manner, and in fact prove q-analogues of the ordinary and shifted hook formulas. The proofs proceed by combining the ordinary, respectively shifted, Hillman–Grassl algorithm and Stanley's (P, ω)-partition theor...

متن کامل

The Inclusion-Exclusion Principle for IF-States

Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events.In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events.Finally, we give some applications of this principle 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

عنوان ژورنال:
  • Discrete Mathematics

دوره 51  شماره 

صفحات  -

تاریخ انتشار 1984