All binomial identities are orderable
نویسنده
چکیده
In this paper we show that all binomial identities are orderable. This is a natural statement from the combinatorial theory of finite sets which additionally has applications in distributed computing. Specifically, we are able to obtain new strong bounds on the round complexity of the weak symmetry breaking task. 1. Preliminaries For any natural number n, we set [n] := {1, . . . , n}. Definition 1.1. A binomial identity is any equality (1.1) ( n a1 ) + · · · + ( n ak ) = ( n b1 ) + · · · + ( n bm )
منابع مشابه
Some Combinatorial Identities and Explanations Based on Occupancy Model
Abstract Some special random variables in occupancy model that balls are distributed into m urns are investigated. The number of occupied urns and the minimal number of balls in all urns are discussed. Some combinatorial identities and their explanations related to the binomial coefficient and Stirling number are derived. Several new infinite summation combinatorial identities on the binomial c...
متن کاملBinomial collisions and near collisions
We describe efficient algorithms to search for cases in which binomial coefficients are equal or almost equal, give a conjecturally complete list of all cases where two binomial coefficients differ by 1, and give some identities for binomial coefficients that seem to be new.
متن کاملThe role of binomial type sequences in determination identities for Bell polynomials
Our paper deals about identities involving Bell polynomials. Some identities on Bell polynomials derived using generating function and successive derivatives of binomial type sequences. We give some relations between Bell polynomials and binomial type sequences in first part, and, we generalize the results obtained in [4] in second part.
متن کاملBinomial Andrews-gordon-bressoud Identities
Binomial versions of the Andrews-Gordon-Bressoud identities are given.
متن کاملSome Identities involving the Partial Sum of q-Binomial Coefficients
We give some identities involving sums of powers of the partial sum of q-binomial coefficients, which are q-analogues of Hirschhorn’s identities [Discrete Math. 159 (1996), 273–278] and Zhang’s identity [Discrete Math. 196 (1999), 291–298].
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 61 شماره
صفحات -
تاریخ انتشار 2017