- I finished my Licenciate in Mathematics in 1967 at
Universidad de Buenos Aires, (Argentina), and
after a period of teaching at Universidad de La Plata, (Argentina, 1967-70),
completed my Ph.D. by 1975 at Rutgers University, (NJ, USA) under the
direction of T. Petrie, (Algebraic and Differential Topology, Equivariant
K-Theory). After being a visiting professor for a year and a half
at the ICMSC, (Universidade de Sao Paulo at Sao Carlos, Brazil),
I taught and researched, from 1977 to 1984, at
Universidade Federal de Santa Catarina, (Brazil), being on leave
one year (1982-1983) to Cambridge University (UK) as a Royal Society visiting
scholar,
occasion in which research in Combinatorial Mathematics captured my attention,
during the Paul Erdos' 70th Anniversary Combinatorial Conference, (whom I had
twice since as a visitor at the University of Puerto Rico).
Since 1984, I perform research in Discrete Mathematics and
teach mainly related graduate courses.
Erdos Number
- My Erdos number (http://www.oakland.edu/enp/Erdos1) is 2 by way of joint papers with the following three
co-authors of the late Paul Erdos (number of joint papers between parentheses):
Carsten Thomassen (1), Alexander Rosa (4) and
Kevin T. Phelps (1).
Mathematical Genealogy
- My Mathematical Genealogy Tree (http://www.genealogy.ams.org/html/id.phtml?id=5831) is,
(with each literal header as a direct descendant from the following one, and
bifurcations -- given by two different thesis supervisors -- as indicated
by accompanying integers):
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A= Italo J. Dejter, Rutgers 1975.
B= Ted Edgar Petrie, Princeton 1964.
C= William Browder, Princeton 1958.
D= John Coleman Moore, Brown 1952.
E= George William Whitehead, Jr., Chicago 1941.
F= Norman Earl Steenrod, Princeton 1936.
G= Solomon Lefschetz, Clark 1911.
H= William Edward Story, Leipzig 1875, (advisers: Neumann and Klein).
-----------------------------------------------------------------------
I1= Carl Neumann, Koenigsberg 1856, (advisers: Richelot and Hesse).
J1= Friedrich Julius Richelot, Koenigsberg 1831.
J1'= Otto Hesse, Koenigsberg 1840.
K1= Karl Gustav Jacob Jacobi, Humboldt-Berlin 1825.
L1= Enno Heeren Dirksen, Gottingen 1820, (advisers: Meyer and Thibaud).
M1= Johann Tobias Meyer d.J. Gottingen 1773.
N1= Abraham Gotthelf Kaestner, Leipzig 1739.
O1= Christian August Hausen, Halle-Wittenberg 1713.
P1= Johann Christoph Wichmannshausen, Leipzig 1685.
Q1= Otto Mencke, Leipzig 1668.
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I2= C. Felix (Christian) Klein, Bonn 1868, (advisers : Plucker and Lipschitz).
J2= Julius Plücker, Marburg 1823.
K2= Christian Ludwig Gerling, Gottingen 1812.
L2= Carl Friedrich Gauß, Helmstedt 1799.
M2= Johann Friedrich Pfaff, , Gottinhen, 1786.
N2= Abraham Gotthelf Kaestner, Leipzig, 1739.
O2= Christian August Hausen, Halle-Wittenberg, 171, Leipzig 1685.
P2= Johann Christoph Wichmannshausen, Leipzig 1685 (=P1).
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J3=Rudolf Otto Sigismund Lipschitz, Berlin 1853, (advisers: Dirichlet and Ohm).
K3= Gustav Peter Lejeune Dirichlet, Bonn 1827, (advisers: Poisson and Fourier).
L3= Simeon Denis Poisson.
L3'= Jean-Baptiste Joseph Fourier.
M3= Joseph Louis Lagrange, (no dissertation, no adviser, but connection to Euler in intellectual herigage).
N3= Leonhard Euler, Basel 1726.
O3= Johann Bernoulli, 1694.
P3= Jacob Bernoulli, 1684.
Q3= Gottfried Wilhelm Leibniz, Altdorf 1666.
R3= Erhard Weigel, Leipzig 1650.
-----------------------------------------------------------------------
K4=Martin Ohm, Erlangen-Nürnberg 1811.
L4=Karl Christian von Langsdorf, Erfurt 1781.
Publications and Student Supervision
- The lists of students that defended their Master dissertations under my
supervision, eleven of them at the Universidade Federal de Santa Catarina (Brazil)
and nineteen of them at my
present location, the University of Puerto Rico (a total of 29 Master theses
supervised), can be found, together with
their titles and dates of defense, respectively
here and here.
- The determination of explicit Hamilton cycles in the
middle levels graph of the Boolean algebra on an odd number n of elements
was first obtained for n less than or equal to 19 in: I.J.Dejter, W.Cedeno
and V.Jauregui, `Frucht Diagrams and Hamilton Cycles', SCIENTIA, Series A:
Mathematical Sciences, volume 5 (1992-1993) 21-37,
MR 1717974 (2001d:05075); 05C25,
item [25] in the list of my publications above,
which can be downloaded here. A note covering
the case n=19 appeared in I.J.Dejter, J. Cordova and J.A> Quintana,
`Two Hamilton cycles in bipartite reflective Kneser graphs', Discrete
Mathematics, 72 (1988) 63-70. More specifically, let i and j be positive
integers and let RG(i,j) be the bipartite graph whose vertices are the i-
and j-subsets of {0,1,...,i+j-1} and whose adjacency is given by inclusion.
The aforementioned paper shows that RG(9,10) and RG(7,9) are hamiltonian.
The first cited paper, shows that together with all simpler cases.
Another paper dealing with these methods: I.J.Dejter, W.Cedeno and
V.Jauregui, `A note on Frucht diagrams, Boolean graphs and Hamilton cycles',
Discrete Mathematics, 114 (1993) 131-135.
A part of this is claimed
as original in a 1999 Congressus Numerantium paper by I.Shields and
C.Savage, seven years later.
- The edge-transitive but not vertex-transitive graph on 112 vertices
reported in a 2005 Journal of Graph Theory paper by M.Conder et al. was
first obtained in
A.E.Brouwer, I.J.Dejter and C.Thomassen, `Highly Symmetric
Subgraphs of Hypercubes', J. Algebraic Combinatorics,
2(1993) 25--29,
MR 1210399 (94c:05037); 05C25 (05C15), item [24] in the list of my
publications above, twelve years earlier. Another view of this
was given in I.J.Dejter, `On symmetric subgraphs of the 7-cube: an overview',
Discrete Mathematics, 124 (1994) 55-66. The construction is traceable
explicitly to I.J.Dejter and P.Guan, `Square-blocking edge subsets in
hypercubes and vertex avoidance', in Graph Theory, Combinatorics,
Algorithms and Applications, Proc. SIAM 2nd Conf. of Graph Theory, Y. Alavi
et al., eds, 1991, 162-174.
