Walter Stromquist's home page

AMSP2012/index.html --- Temporary link for AMSP students (till end of July, 2012)

Go to my Research and publications page
Go to the official Mathematics Magazine page (MAA)
Go to the Hughes-Carpenter family directory page (password required)
Go to my Bradshaw family history page
Go to my Swarthmore College page (out of date)
See photos from the 315th Engineering Battalion, 90th Infantry Division in WW2.
Send me email at

A Bidding Model for Auctions of Offshore Energy Sites
A presentation at the Eastern Economic Association, March 1, 2009, by Radford Schantz and WRS
Paper (pdf) and Powerpoint presentation (2003 ppt format)

Two recent presentations on pies and cakes:
Cutting a Pie is Not a Piece of Cake - presented at the World Congress of the Game Theory Society, Northwestern University, Evanston, IL, July 13, 2008. Reports Joint work with Julius Barbanel and Steven Brams, to appear in the American Mathematical Monthly in 2009.
CakesPies.ppt - presentation to the graduate combinatorics seminar at Rutgers University, October 4, 2007.


Fair division: Both of the following papers are also available as part of Dagstuhl Seminar Proceedings 07261 (link to Dagstuhl's archive).

"A pie that can't be cut fairly" (10-page pdf)---paper for the Dagstuhl Seminar Proceedings, giving an example of three measures on a pie for which there is no division that is both envy free and undominated. Earlier versions (from the Seminar on Fair Division, June, 2007): Abstract (1-page pdf), Paper (11-page pdf), Presentation (PowerPoint presentation).

"Envy-free cake divisions cannot be found by finite protocols (9-page pdf)---For the same Proceedings, this paper shows that no finite protocol can guarantee to find an envy-free division of a cake among three claimants, if each is to receive a single connected piece. Earlier version (from the Seminar): FiniteMethods.pdf.

Here are materials for participants in the MAA Minicourse on Mathematical Finance presented January 5 and 7, 2005 at the mathematics meetings in Atlanta, GA, AND August 4-5, 2005 at the Mathfest in Albuquerque, NM.

Also, here is a PowerPoint presentation about packing densities from the conference on Graph Theory With Altitude, May 17-20, 2005.

...and a more narrowly-focused PowerPoint presentation about packing rates of measures and the packing density of the pattern 2413 from the Permutation Patterns 2007 conference, June 11-15, 2007.

POSETS.DOC --- Here is a 1993 memorandum on packing densities of layered patterns (WORD document with graphics, 10 pages). It is the final version, and also the version that has been cited in various subsequent publications. It includes a detailed verification of the packing density of 132, but its main theorem is that layered permutaions (resp. posets) have layered permutations (resp. posets) as optimizers. The best current proof of this result (based on ideas in Reid Barton's Morgan Prize paper) is in the "DensitiesAtAltitude" presentation (above).

Link to my web page at Swarthmore College (mostly just for this semester's classes): has gone out of the personal webpage business, so our family website is in flux. For the time being, here is the the Hughes-Carpenter Family Directory Page (password required) and here is our page of Bradshaw family history (no password needed) which includes a link to the Bradshaw family Bible.

Here are two photographs from the 315th Engineering Battalion, 90th Infantry Division in WW2.

You can send me email at