Analysis of the Gift Exchange Problem

  title={Analysis of the Gift Exchange Problem},
  author={Moa Apagodu and David L. Applegate and N. J. A. Sloane and Doron Zeilberger},
  journal={Electron. J. Comb.},
In the gift exchange game there are $n$ players and $n$ wrapped gifts. When a player's number is called, that person can either choose one of the remaining wrapped gifts, or can "steal" a gift from someone who has already unwrapped it, subject to the restriction that no gift can be stolen more than a total of $\sigma$ times. The problem is to determine the number of ways that the game can be played out, for given values of $\sigma$ and $n$. Formulas and asymptotic expansions are given for these… 

Tables from this paper

Gift-exchange Game Theory for Gamification on Digital Data Collection Systems

The results indicate a significant increase in user involvement in the implementation of gamification with GEG, raising the opinion that the need to use game theory in gamification to improve user interaction on the system.

8 M ar 2 01 8 Restricted lonesum matrices

Lonesum matrices are matrices that are uniquely reconstructible from their row and column sum vectors. These matrices are enumerated by the poly-Bernoulli numbers; a sequence related to the multiple

Restricted lonesum matrices

This paper studies lonesum matrices with restriction on the number of columns and rows of the same type with rich literature in number theory.



The Gift Exchange Problem

The aim of this paper is to solve the “gift exchange” problem: you are one of n players, and there are n wrapped gifts on display; when your turn comes, you can either choose any of the remaining

Restricted Partitions of Finite Sets

In this paper we consider the following combinatorial problem. In how many ways can n distinguishable objects be placed into an unrestricted number of indistinguishable boxes, if each box can hold at

A Course of Modern Analysis

The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.

An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities

SummaryIt is shown that every ‘proper-hypergeometric’ multisum/integral identity, orq-identity, with a fixed number of summations and/or integration signs, possesses a short, computer-constructible

Resurrecting the asymptotics of linear recurrences

The J.C.P. miller recurrence for exponentiating a polynomial, and its q- analog *

J.C.P's Miller ‘symbolic exponentiation’ algorithm is exposited and a q-analog is given. It is pointed out that these simple method, that usesdifference equations in an essential way, are superior to

The Method of Differentiating under the Integral Sign

On Solutions of xd = 1 In Symmetric Groups

  • L. Moser
  • Mathematics
    Canadian Journal of Mathematics
  • 1955
1. Introduction. Several recent papers have dealt with the number of solutions of xd = 1 in Sn, the symmetric group of degree n. Let us denote this number by An,d and let An,2 = Tn.

A maple program that finds, and proves, recurrences and differential equations satisfied by hyperexponential definite integrals

In [A-Z], an algorithm that given a hyperexponential function of two variables F(x,y), produces a differential equation satisfied by the inequality of the following type: For α ≥ 1, β ≥ 1 using LaSalle's inequality.