Some Combinatorial Identities and Explanations Based on Occupancy Model
نویسنده
چکیده
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 coefficients are obtained.
منابع مشابه
On the Properties of Balancing and Lucas-Balancing $p$-Numbers
The main goal of this paper is to develop a new generalization of balancing and Lucas-balancing sequences namely balancing and Lucas-balancing $p$-numbers and derive several identities related to them. Some combinatorial forms of these numbers are also presented.
متن کاملAnalysis of Depression based on Meta-Ethics
Background: One of the most important issues that requires more attention is the role of philosophy in individual and social life. Although sciences such as psychology and sociology propose their theories based on philosophical foundations, the role of philosophy as a field which can be influential in solving humans’ problems is not paid due attention. One of the sciences where philosophy can h...
متن کاملOn Series Expansions of Capparelli’s Infinite Product
Using Lie theory, Stefano Capparelli conjectured an interesting Rogers-Ramanujan type partition identity in his 1988 Rutgers Ph.D. thesis. The first proof was given by George Andrews, using combinatorial methods. Later, Capparelli was able to provide a Lie theoretic proof. Most combinatorial Rogers-Ramanujan type identities (e.g. the Göllnitz-Gordon identities, Gordon’s combinatorial generaliza...
متن کاملHeat Traces on Spheres and Combinatorial Identities
Abstract. We present a concise explicit expression for the heat trace coefficients of spheres. Our formulas yield certain combinatorial identities which are proved following ideas of D. Zeilberger. In particular, these identities allow to recover in a surprising way some known formulas for the heat trace asymptotics. Our approach is based on a method for computation of heat invariants developed...
متن کاملCombinatorial Proofs of q-Series Identities
We provide combinatorial proofs of six of the ten q-series identities listed in [3, Theorem 3]. Andrews, Jiménez-Urroz and Ono prove these identities using formal manipulation of identities arising in the theory of basic hypergeometric series. Our proofs are purely combinatorial, based on interpreting both sides of the identities as generating functions for certain partitions. One of these iden...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011