# Mathematics

*Early research on non-linear differential equations was succeeded by a long period of work on linear and integer programming and on combinatorial problems.*

**Origin and Early Evolution of Corner Polyhedra** European Journal of Operational Research, Volume 253, Issue 3, pages 543-556, (16 September 2016)

**Forty Years of Corner Polyhedra **Lecture, 12th Combinatorial Optimization Workshop, Aussois, France, January 8, 2008

**Corner Polyhedra** Lecture, George Nemhauser Symposium, Georgia Tech, June 26-27, 2007

**Thoughts About Integer Programming** Lecture, University of Montreal, January 26, 2007

**The Atoms of Integer Programming** *Annals of Operations Research.* 149, pp. 99–102 (2007)

**Cyclic Group and Knapsack Facets** Julian Araoz, Lisa Evans, Gomory, R. E., Johnson, E. L. *Mathematical Programming*. Ser.B 96: Springer-Verlag, pp. 377-408 (2003).

**Corner Polyhedra and their Connections with Cutting Planes** Gomory, R. E., Johnson, E.L. Lisa Evans. *Mathematical Programming*. Ser.B 96: Springer-Verlag, pp. 321-339 (2003).

**T-space and Cutting Planes** Gomory, R. E., Johnson, E.L.* Mathematical Programming*. Ser. B 96: Springer-Verlag, pp. 341-375 (2003).

**Delays at Toll Booths – Why Wait in Line?** (with Denos C. Gazis), *Transportation Quarterly*. Spring 1994, Vol 48, No. 2, pp. 107-114.

**Early Integer Programming ***History of Mathematical Programming*. Edited by J. K. Lenstra, A. H. G. Rinnooy Kan, and A. Schrijver, Elsevier Science Publishers B.V., Amsterdam, 1991, pp. 55-61.

**Multi-Terminal Flows in a Network** (with T. C. Hu), *Studies in Graph Theory, Vol. 11, Part 1*, edited by D. R. Fulkerson, The Mathematical Association of America, 1975, pp. 172-199.

**R-Separating Sets** (with T.C. Hu and J. M. Yohe), *Canadian Journal of Mathematics*, Vol. XXVI, No. 6. 1974, pp. 1418-1429.

**The Group Problems and Subadditive Functions** (with Ellis L. Johnson), *Mathematical Programming*. Academic Press, 1973, pp. 157-184.

**Some Continuous Functions Related to Corner Polyhedra, Part II** (with Ellis L. Johnson), *Mathematical Programming*, Vol. 3, No. 3. North-Holland, December 1972, pp. 359-389.

**Some Continuous Functions Related to Corner Polyhedra, Part I** (with Ellis L. Johnson), *Mathematical Programming*, Vol. 3, No. 1. North-Holland, August 1972, pp. 23-85.

**Properties of a Class of Integer Polyhedra** *Integer and Non-Linear Programming*. Edited by J. Abadie. North-Holland, 1970, pp. 353-365.

**Some Polyhedra Related to Combinatorial Problems** *Journal of Linear Algebra and Its Applications*, Vol. 2, No. 4. October 1969, pp. 451-558; also published in *Combinatorial Structures and Their Applications, Proceedings of the Calgary International Conference on Combinatorial Structures and their Applications*, held at the University of Calgary, Calgary, Alberta, Canada, June 1969. New York, Gordon and Breach, 1970, p. 117.

**Flows in Continua** Sildenafil citrate *Integer Programming and Network Flows*, Chapter 12 (with T. C. Hu). Addison-Wesley Publishing Co., 1969, pp. 214-228.

**Post-Doctoral Experience** *Proceedings of Conference on Education in Applied Mathematics sponsored by SIAM under a grant of NSF*, Aspen, Colorado, May 24-27 1966,* SIAM Review*, Vol. 9, No. VI. April 1967, pp. 388-396 (discussion pp. 396-410).

**Faces of an Integer Polyhedron** *Proceedings of the National Academy of Sciences*, Vol. 57, No. 1. January 1967, pp.16-18; also published in *Lectures in Applied Mathematics 2, Part I, Mathematics of the Decision Sciences*. Ed. by G. B. Dantzig and A.F.Veinott, Jr., American Mathematical Society, 1968, pp. 283-287.

**The Theory and Computation of Knapsack Functions** (with P. C. Gilmore), *Operations Research*, Vol. 14, No. 6. November-December 1966, pp. 1045-1074.

**On the Relation Between Integer and Non-Integer Solutions To Linear Programs** *Proceedings of the National Academy of Sciences*, Vol. 53, No. 2. February 1965, pp.260-265; also published in *Lectures in Applied Mathematics, 2, Part I, Mathematics of the Decision Sciences*. Ed. by G. B. Dantzig and A. F. Veinott, Jr., American Mathematical Society, 1968, pp. 288-294.

**Optimal Programming of Lot Sizes, Inventories and Labor Allocations** (with B. P. Dzielinski), *Management Sciences*, Vol. 11, No. 9. July 1965, pp. 874-890.

**The Traveling Salesman Problem ***Proceedings of IBM , Scientific Computing Symposium on Combinatorial Problems*, March 1964, IBM Data Processing Division (White Plains, NY), 1966, pp. 93-121.

**Mathematical Programming** *American Mathematical Monthly*, Vol. 72, No. 2. Pt. 2. February 1965, pp. 99-110.

**Sequencing a One State-Variable Machine: A Solvable Case of the Traveling Salesman Problem** (with P. C. Gilmore), *Operations Research*, Vol. 12, No. 5. September-October 1964, pp. 655-679.

**Multi-Stage Cutting Stock Problems of Two and More Dimensions** (with P. C. Gilmore), *Operations Research*, Vol.13, No. 1. January-February 1965, pp. 94-120.

**Automatic Design of Optimal Structures** with W. S. Dorn and H. J. Greenberg),* Journal de Mecanique,* Vol. 3, No. 1. March 1964, pp. 25-52.

**A Solvable Case of the Traveling Salesman Problem** (with P. C. Gilmore),* Proceedings of the National Academy of Sciences*, Vol. 51, No. 2. February 1964, pp. 178-181.

**A Linear Programming Approach to the Cutting Stock Problem — Part II** (with P. C. Gilmore), *Operations Research*, Vol.11, No.6. November-December, 1963, pp. 863-888.

**Some Properties of the Rank and Invariant Factors of Matrices** (with A. J. Hoffman and N. C. Hsu), *Canadian Mathematical Bulletin*, Vol. 7, No. 1. January 1964, pp. 85-96.

**Synthesis of a Communication Network** (with T. C. Hu), *SIAM Journal*, Vol. 12, No. 2. June 1964, pp. 348-369.

**Analysis and Synthesis of Communication Networks** (with R. T. Chien and T. C. Hu), IEEE Transactions on Circuit Theory, Vol. CT-11, No. 1, March 1964, pp. 19-22.

**A Primal Method for the Assignment and Transportation Problems** (with Michel L. Balinski), *Management Science*, Vol. 10, No. 3. April 1964, pp. 578-593.

**Large and Non-Convex Problems in Linear Programming** *Proceedings of the Symposium on the Interactions between Mathematical Research and High-Speed Computing of the American Mathematical Society*, Vol. XV. 1963, pp. 125-139.

**An Algorithm for Integer Solutions to Linear Programs** *Recent Advances in Mathematical Programming.* Edited by Robert L. Graves and Philip Wolfe, McGraw-Hill, 1963, pp. 269-302.

**All-Integer Integer Programming Algorithm** *Industrial Scheduling*. Edited by John F. Muth and Gerald L. Thompson, Prentice-Hall, 1963, pp. 193-206.

**A Mutual-Primal-Dual Simplex Method** (with Michel L.Balinski), *Proceedings of Mathematical Programming Symposium*, 1963, pp. 17-26.

**On the Convergence of an Integer-Programming Process** (with A. J. Hoffman), *Naval Research Logistics Quarterly*, Vol. 10, No. 2. June 1963, pp. 121-123.

**The Trim Problem*** IBM Systems Journal*, September 1962, pp. 77-82.

**“Finding Optimum Combinations,”** (with A. J. Hoffman), *Inter-national Science and Technology*, July 1962, pp. 26-33.

**An Application of Generalized Linear Programming to Network Flows** (with T. C. Hu), *Journal of the Society for Industrial and Applied Mathematics*, Vol. 10, No. 2. June 1962, pp. 260-283.

**Multi-Terminal Network Flows** (with T. C. Hu), *Journal of the Society for Industrial and Applied Mathematics*, Vol. 9, No. 4. December 1961, pp. 551-570.

**A Linear Programming Approach to the Cutting Stock Problem** (with P. C. Gilmore), *Operations Research*, Vol. 9, No. 6. November-December 1961, pp. 849-859.

**Integer Programming and Pricing **(with William J. Baumol), *Econometrica*, Vol. 28, No. 3. July 1960, pp. 521-550.

**Solving Linear Programming Problems in Integers** *Proceedings of Symposia in Applied Mathematics*, Vol. 10. July 1960, pp. 211-215.

**Outline of an Algorithm for Integer Solutions to Linear Programs** *Bulletin of the American Mathematical Society*, Vol. 64, No. 5. September 1958, pp. 275-278.

**Critical Points at Infinity and Forced Oscillation** Contributions to the Theory of non-Linear Oscillations, Vol. 3, *Annals of Mathematics*, Study 36. Princeton University Press, 1956, pp. 85-126.

**A Study of Trajectories Which Tend to a Limit Cycle in 3-Space** (with F. Haas), *Annals of Mathematics*, Vol. 62, No. 1. July 1955, pp. 152-161.

**Trajectories Tending to a Critical Point in 3-Space ***Annals of Mathematics*, Vol. 61, No. 1. January 1955, pp.140-153.

**Boundaries for the Limit-Cycle of Van der Pol’s Equation** (with D. E. Richmond), *Quarterly of Applied Mathematics*,Vol. IX, No. 2. July 1951, pp. 205-209.