Vol. 11, No. 5, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11
Issue 5, 721–900
Issue 4, 541–720
Issue 3, 361–540
Issue 2, 181–359
Issue 1, 1–179

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors’ Addresses
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Enumeration of stacks of spheres

Lauren Endicott, Russell May and Sienna Shacklette

Vol. 11 (2018), No. 5, 867–875
Abstract

As a three-dimensional generalization of fountains of coins, we analyze stacks of spheres and enumerate two particular classes, so-called “pyramidal” stacks and “Dominican” stacks. Using the machinery of generating functions, we obtain exact formulas for these types of stacks in terms of the sizes of their bases.

Keywords
enumerative combinatorics, generating functions
Mathematical Subject Classification 2010
Primary: 05A15
Milestones
Received: 11 May 2017
Revised: 14 September 2017
Accepted: 17 September 2017
Published: 2 April 2018

Communicated by Glenn Hurlbert
Authors
Lauren Endicott
The Craft Academy for Excellence in Science and Mathematics
Morehead State University
Morehead, KY 40351
United States
Russell May
Department of Mathematics and Physics
Morehead State University
Morehead, KY 40351
United States
Sienna Shacklette
The Craft Academy for Excellence in Science and Mathematics
Morehead State University
Morehead, KY 40351
United States