Marty Lewinter
Professor of Mathematics, Computer Science, and New Media
at Purchase College (SUNY)
Ph.D. in Mathematics - CUNY Graduate Center
M.F.A. in Music - Purchase College
Phone: (914) 251 - 6680
Office: NS3005
Office Hours: TBA
Weekly Study Session: TBA
Research Interests: My research interests are graph theory, classical differential geometry, and number theory. I enjoy reading and lecturing about the history of mathematics. Most of my publications are in graph theory and fall into three categories: spanning trees, distance problems, and hypercubes. As graph theory is accessible to undergraduates, some of my publications are co-authored by students.
Click here for a list of my publications with students or former students
Hobbies: My non-mathematical interests include Objectivism (the philosophy of Ayn Rand), shotokan karate (which I teach at the college in the Gym, Rm. 0006), and guitar (classical and pop). I compose classical and popular music. I also write classical-style poetry (that is, poetry with rhyme and meter).
Click here for samples of my poetry and compositions
Here's one:
From Where Springs Your Pride?
Unafraid because you're unaware of the threat?
Do you mock death because you haven't seen it yet?
Defy you the foe from safe castle wall?
Climb only when the net catches your fall?
Are you the confident master of routine,
Smiling 'cause your world hasn't been cold and mean?
Untested, untried?
From where springs your pride?
If from good looks or youth,
Then heed well this truth:
To see the threat,
Yet to double your bet,
To stare death in the face
And remain in the race,
Fighting your foe in his domain,
Scaling the cliff though they call you insane.
To shun routine and master the new,
To bravely smile when they've made fun of you,
To sing your battle cry out loud
And earn for yourself the right to be proud.
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Publications
1. M.Lewinter, Spanning trees of product graphs. Cong. Num. 54 (157‑161) 1986.
2. M.Lewinter, Graph Theory. Monographs in Undergrad. Math.,13, JUM, Guilford, NC, 1986.
3. F.Harary and M.Lewinter, Hypercubes and other recursively defined hamilton-laceable graphs. Cong. Num. 60 (81‑84) 1987.
4. M.Lewinter, Interpolation theorem for the number of degree‑-preserving vertices of spanning trees. IEEE Trans.Circuits and Systems, CAS‑34,( 205) 1987.
5. M.Lewinter and W.Widulski, Which two‑legged caterpillars span hypercubes? GTN of NY XIV (30-32) 1987.
6. M.Lewinter and M.Migdail-Smith, Degree‑preserving vertices of spanning trees of the hypercube. GTN of NY XIII (26‑27) 1987.
7. M.Lewinter, Which caterpillars span a hypercube? GTN of NY XIII (23‑25) 1987.
8. F.Buckley and M.Lewinter, On graphs with center-preserving spanning trees. GTN of NY XIV (33‑35) 1987.
9. M.Lewinter, Problems in classical differential geometry. Monographs in Undergraduate Mathematics, Vol. 14, JUM, Guilford, NC, 1987.
10. F.Buckley and M.Lewinter, A note on graphs with diameter‑preserving spanning trees. J.Graph Theory, 12 (525‑528) 1988.
11. F. Harary and M. Lewinter, The starlike trees which span a hypercube. Comput. Math. Appl., 15 (299-302) 1988.
12. F.Harary and M.Lewinter, Spanning subgraphs of a hypercube II: Double starlike trees. Mathl. Comput. Modelling, 1 (216-217) 1988.
13. F.Harary and M.Lewinter, Spanning subgraphs of a hypercube III: Meshes. Intern.J.Computer Math., 25(1‑4) 1988.
14. M.Lewinter, The diameter of the complement of a regular graph. Cong. Num. 64 (157‑158) 1988.
15. F.Harary, M.Lewinter, and W.Widulski, On two‑legged caterpillars which span hypercubes. Cong. Num. 66 (103‑108) 1988.
16. S.Arengo and M.Lewinter, How connected are product graphs? GTN of NY XVI (14‑15) 1988.
17. M.Lewinter, Embedding meshes in hypercubes. GTN of NY XV (21-22) 1988.
18. M.Lewinter, Graph Theory II. Monographs in Undergraduate Mathematics, Vol. 13, JUM, Guilford, NC, 1988.
19. F.Buckley and M.Lewinter, Minimal graph embeddings, eccentric vertices and the peripherian. Proc. 5th Carib. Conf. Comb.& Comp.(72‑84) 1988.
20. G.Capriulo, D.Lints, and M.Lewinter, Ingestion rate and body size in phagotrophic organisms. Can. J. Zool., 68 (313‑317) 1989.
21. F.Harary and M.Lewinter, Spanning subgraphs of a hypercube V: Spanned subcubes. Annals NY Academy of Sciences, 576 (219‑225) 1989.
22. J.Gratt and M.Lewinter, The eccentricities of a center‑preserving spanning tree. GTN of NY XVII (18-19) 1989.
23. R.Depalma and M.Lewinter, Which starlike trees span n-‑meshes? GTN of NY XVII (12‑15) 1989.
24. M.Lewinter and W.Widulski, Which trees span the ternary cubes? GTN of NY XVII (16‑17) 1989.
25. C.Camazine and M.Lewinter, Center‑distance sets of F ‑graphs. GTN of NY XVII (10-11) 1989.
27. A.Fox, D.Gagliardi, M.Lewinter and W.Widulski, What is the minimum label number of U x V ? GTN of NY XIX (38-39) 1990.
28. M.Haag and M.Lewinter, Double embeddings of a graph in the hypercube. GTN of NY XX (50-51) 1991.
29. F.Harary and M.Lewinter, Spanning subgraphs of a hypercube VI: Survey and unsolved problems. Graph Theory, Combinatorics, and Applications, edited by Y.Alavi et al. J.Wiley NY (633-637) 1991.
30. N.Highstein and M.Lewinter, The euler number of a graph II. GTN of NY XIX (52‑53) 1991.
31. M.Lewinter and W.Widulski, Equipartition sets of hypercubes. J. Comb. Info. & System Sci. 16 (19‑24) 1991.
32. T.Bocchi and M.Lewinter, Classification of L-‑graphs. GTN of NY XXIII (29‑32) 1992.
33. T.Bocchi and M.Lewinter, How many 4‑cycles does a spanning tree of M(m, n) span? GTN of NY XXIII (33‑34) 1992.
34. M.Lewinter and W.Widulski, Which double starlike trees span ladders? Annals of Discrete Math, 55 (327-332) 1993.
35. F.Harary and M.Lewinter, Which graphs are pluperfect? Australasian Journal of Combinatorics, 7 (81-86) 1993.
36. M.Lewinter, Graphs with special distance properties. Annals of Discrete Math, 55 (89-92) 1993.
37. F.Buckley and M.Lewinter, Graphs with all diametral paths through distant central nodes. Mathl. Comput. Modelling, 11 (35‑41) 1993.
38. F.Harary, T.Haynes and M.Lewinter, On the codomination number of graphs. Proyecciones, 12, 2 (149‑153) 1993.
40. M.Lewinter and W.Widulski, Minimal hyper‑hamiltonian-laceable graphs. Mathl. Comput. Modelling, 17 (125‑127) 1993.
41. F.Harary and M.Lewinter, All hypercubes are pluperfect. Bull.Malaysian Math. Soc. 16 (21‑23) 1993.
42. T.Bocchi and M.Lewinter, Maximal planar eulerian graphs. GTN of NY XXIV (47-50) 1993.
43. M.Aaron and M.Lewinter, 0‑deficient vertices of spanning trees. GTN of NY XXVII (31-32) 1994.
44. T.Bocchi, D.Gagliardi and M.Lewinter, k ‑deficient spanning trees. GTN of NY XXIX (42-43) 1995.
45. T.Bocchi, D.Gagliardi and M.Lewinter, Reach-‑preserving properties of product graphs. GTN of NY XXIX (40‑41) 1995.
46. D.Gagliardi, F.Harary and M.Lewinter, A lower bound for the number of irregular multi‑graphs. GTN of NY XXXI (6-8) 1996.
47. D.Gagliardi and M.Lewinter, An interpolation theorem for the maximum deficiencies of spanning trees. GTN of NY XXX (37) 1996.
48. M.Lewinter and W.Widulski, Hyperhamilton-laceable and caterpillar-spannable product graphs. Mathl. Comput. Modelling, 34, (99-104) 1997.
49. D.Gagliardi and M.Lewinter, An infinite class of reach-preservable graphs. Networks, 29 (217‑218) 1997.
50. M.Lewinter, Distance, spanning trees and hypercubes: new and old results. GTN of NY XXXII (42‑46) 1997.
51. D.Aulicino and M.Lewinter, k-equidistant sets of Qn . GTN of NY XXXVI (17-19) 1999.
53. D.Aulicino and M.Lewinter, Almost all meshes are pancentral. GTN of NY XXXIX (38-40) 2000.
54. T.Bocchi, M.Lewinter, A.Silverman, Factoring degree sequences. GTN of NY XLI (24-25) 2001.
55. M.Gargano, M.Lewinter and J.Malerba, Paintable graphs. Cong. Num. 148, (169-175) 2001.
56. D.Aulicino and M.Lewinter, Pancentral graphs. Cong. Num. 150, (69-72) 2001.
57. M.Gargano, M.Lewinter and J.Malerba, Problems and Solutions, Problem #353, Math.Teachers' Journal, Vol. 51, 3, 2001.
58. S.Karimi, M.Lewinter and J.Stauffer, Double bonds in hexacyclic hydrocarbons and maximal planar graphs. GTN of NY XLIII (9-11) 2002.
59. M.Lewinter and W.Widulski, The Saga of Mathematics : A Brief History. Prentice-Hall, 2002.
60. F.Buckley and M.Lewinter, A Friendly Introduction to Graph Theory. Prentice-Hall, 2003.
61. M.Gargano, M.Lewinter and J.Malerba, Hypercubes and Pascal's triangle: A tale of two proofs. Math. Magazine, Vol.76, 3 (216-217) 2003.
62. S.Karimi, M.Lewinter and J.Stauffer, Double bonds in fused hexacyclic systems. J.Math.Chem., 34, (297-301) 2003.
63. M.Gargano, M.Lewinter and J.Malerba, On the number of increasing nonconsecutive paths and cycles in labeled graphs. GTN of NY XLIV (8-9) 2003.
64. T.Bocchi, S.Karimi, and M.Lewinter, On the distribution of pi bonds in cyclofusene. J.Math.Chem., 35, (339-344) 2004.
65. D.Gagliardi, H.Tyler, M.Lewinter, Three-colorable maximal planar graphs and self-complementary graphs. GTN of NY XLVII (40-41) 2004.
66. F.Buckley and M.Lewinter, CHINESE TRANSLATION OF A Friendly Introduction to Graph Theory. 2005.
67. M.Lewinter and W.Widulski, KOREAN TRANSLATION OF The Saga of Mathematics : A Brief History. 2005.
68. S.Karimi and M.Lewinter, Interpolation of shared pi-bonds in cyclofusene. J.Math.Chem., 38, (103-106) 2005.
69. M.Gargano, M.Lewinter, J.Malerba, A.Weisenseel, Discrete renyi parking constants. Cong. Num. 176, (43-48) 2005.
70. S.Karimi and M.Lewinter, On the properties of convex multilayered cyclofusene. J.Math.Chem., 39, (593-596) 2006.
71. D.Gagliardi and M.Lewinter, A survey of undergraduate research in graph theory. GTN of NY. To appear.
72. M.Huang and M.Lewinter, The four-cycles of a directed mesh. GTN of NY L . To appear 2006.