## Research and Publications

## Combinatorics: Coloring Maps

WRS

**The Four Color Theorem for Small Maps**

*J. Comb. Theory B* 19 (1975) 256-268.

WRS

**Some Aspects of the Four Color Problem**

Thesis, Harvard University, 1975. Advisor: Professor Andrew Gleason.

(The link is to a 7MB pdf file made by scanning the typed pages.)

WRS

**The Four Color Theorem for Locally Planar Graphs (problem statement)**

*Graph Theory and Related Topics,* Bondy and Murty (eds.), Academic Press (1979).

Michael O. Albertson and WRS

**Locally Planar Toroidal Graphs are 5-Colorable,**

*Proceedings of the American Mathematical Society* 84 (1982) 449-456 (JSTOR link).

## Combinatorics: Combinatorial Games

WRS and D. Ullman

**Sequential Compounds of Combinatorial Games**

*J. Theoretical Computer Science* 119(2) (October 25, 1993) 311-321.

D. Loeb, A. J. S. Lazarus, J. Propp, WRS, and D. Ullman

**Combinatorial Games under Auction Play**

*Games and Economic Behavior* 27(2) (May, 1999) 229-264.

WRS

**Winning Paths in N-by-Infinity Hex**

*Integers* 7 (2007) G5

## Combinatorics: Permuation Patterns

WRS

**Packing layered posets into posets**

July 18, 1993 memorandum (Word document with graphics, 10 pages)

M. H. Albert, M. D. Atkinson, C. C. Handley, D. A. Holton, WRS

**On Packing Densities of Permutations**

*Electronic Journal of Combinatorics* 9(1) (2002) R5 (link is to pdf at EJC).

WRS

**Densities at Altitude** (ppt)

Presentation at "Graph Theory With Altitude" conference, 2005.

Alexander Burstein, Matthieu Josuat-Vergès, and WRS

**New Dumont permutations**,
*Pure Mathematics and Applications* **21** (2010) 177-206.

This paper incorporates an earlier version by Alexander Burstein and WRS,

**Dumont permutations of the third kind,** presented by the first author at FPSAC 2007.

Cathleen Battiste Presutti and WRS

**Packing rates
of measures and a conjecture for the packing density of 2413**

In
Permutation Patterns (2010), S. Linton, N. Ruškuc, and V. Vatter, Eds.,
vol. 376 of

London Math. Soc. Lecture Note Series,
Cambridge University Press, pp. 3-40.

(First link is to PowerPoint presentation from
Permutation Patterns 2007 conference,

St. Andrews, Scotland, June, 2007.)

## Fair Division

WRS

**How to Cut a Cake Fairly**

*American Mathematical Monthly* Note, 87 (October, 1980) 640-644.
Also addendum,
October 1981 (JSTOR links).

WRS and D. R. Woodall

**Sets on which Several Measures Agree**

*J. Math. Analysis and Applications* 108 (1985) 241-248.

WRS

**A pie that can't be cut fairly**

Dagstuhl Seminar Proceedings 07261, Seminar on Fair Division, June, 2007.

That link is to Dagstuhl's archive. **Local Link.** Earlier version from seminar: **Abstract**, **Paper**, and **Presentation**.

Julius Barbanel, Steven J. Brams, and WRS

**Cutting a pie is not a piece of cake**

*American Mathematical Monthly* 116 (2009) 496-514.

WRS

**Envy free cake divisions cannot be found by finite protocols**

*Electronic Journal of Combinatorics* 15(1) (2008) R11.

Earlier versions: Dagstuhl Seminar Proceedings 07261 and conference version (June, 2007).

## Geometry and Topology

WRS

**The Maximum Distance Between Two-Dimensional Banach Spaces**

*Mathematica Scandinavica* 48 (1981) 205-225.

WRS

**Packing Unit Squares Inside Squares - I, - II,
- III.**

Unpublished memoranda 1984-85. (Version published in EJC, 2003. The original memoranda support results in EJC's DS7, a dynamic survey by E. Friedman.)

WRS

**Inscribed Squares in Closed Curves**

*Mathematika* 36 (1989) 187-197.

Jonathan Ashley, Branko Grünbaum, G. C. Shephard, and WRS

**Self-duality groups and ranks of selfdualities**

*Applied geometry and discrete mathematics* (the Victor Klee Festschrift)

AMS: DIMACS series on Discrete Mathematics and Theoretical Computer Science 4 (1991) 11-50.

WRS

**Classification of Self-Dual Tilings**

preprint, Special Session on Tilings, AMS Philadelphia meeting, 1991

WRS

**Packing 10 or 11 Unit Squares in a Square**

*Electronic J. of Combinatorics* 10(1) (2003) R8.

## Applications: Tax Analysis

WRS

**Federal Income Tax Treatment of Married and Single Taxpayers**

Special Report, 8 Tax Notes 731 (June 11, 1979). Reprinted in *25 Years of Tax Notes,* Tax Analysts, 1997 (local pdf link).

Roy A. Wyscarver with contibutors Ralph B. Bristol, Brenda G. James, WRS, Ben Okner

**The Treasury Personal Individual Income Tax Model** (local pdf link)

Published as OTA Paper 32 by the
Office of Tax Analysis, Treasury Department, July, 1978.

Treasury Department (WRS among acknowledged contributors)

**Blueprints for Basic Tax Reform**

Treasury Department, January 17, 1977 (Treasury link).

## Applications: Search and Tracking

WRS and L. D. Stone

**Constrained Optimization of Functionals with Search Theory Applications**

*Math. of Operations Research* 6 (1981) 518-529.

B. Belkin and WRS

**The Need for Multiple-Hypothesis Data Correlation Methods in Multi-Target Tracking**

*Proceedings of the 8th MIT/ONR Workshop on C3 Systems,* 1985.

WRS

**Practitioner's Commentary: The Drug-Running Papers**

*UMAP Journal,* December, 1988. Reprinted in "MCM: The First Ten Years," *UMAP Journal* Special Edition, COMAP, 1994.

C. A. Mauro and WRS

**Probabilistic Treatment of Discrete Attributes in Correlation**

*Proc. Tri-Service Combat Identification Systems Conference (CISC-89),* 1989.

G. Schweiter and WRS

**The Effect of Sensor Quality on Tracker/Correlator Performance**

*Proc. Tri-Service Data Fusion Symposium,* 1990.

## Applications: Risk Management

WRS

**Roots of Transition Matrices**

Memorandum for Larry Forest, April 24, 1996.

This is the paper cited by Bluhm, Overbeck, and Wagner in *An Introduction to Credit Risk Modeling* (Chapman & Hall) and some web publications.

WRS

**Uses and Limitations of Risk Analysis - Web (html) or
Word (.doc)**

Proceedings of the Risk Analysis Seminar, Royal Commission on the Ocean Ranger Marine Disaster, 1984.

WRS

**Financial minicourse notes**

From minicourse presented most recently at 2005 national meetings and 2005 Mathfest.

## Other Topics

T. Andreescu, WRS, and Z. Sunik

**Bandwidth Reduction Number of Square Grids**

*Algebra and Discrete Mathematics* 2 (2007) 1-15. Also
earlier version:
arxiv.org/abs/math.CO/0305365, 26 May 2003.

WRS

**Computing the Best Isotonic Approximation to a Function**

Eugene Lukacs Symposium on Order-Restricted Inference, Bowling Green University, 1992.

R. C. Marshall, M. C. Meurer, J. F. Richard, and WRS

**Numerical Analysis of Asymmetric First Price Auctions**

*Games and Economic Behavior* 7 (1994) 193-220.

WRS

**Modeling response to proposed OCS leasing schedules**

Abstract of presentation, *AAPG Bulletin*, American Assoc. of Petroleum Geologists 71(5) (May, 1987) 619.