Jorge Luis Ramírez Alfonsín

Sharing jugs of wine

Abstract Two people have a full B -gallon jug of wine and two empty jugs of capacity M and S , respectively, where B = M + S . Any jug may be poured into any other jug until either the first one is empty or the second is full. What is the quickest way for them to divide the wine equally? We solve this problem and show that a natural related problem may be solved in polynomial time.

Combinatorial geometries

This special volume is dedicated to the memory of late Michel Las Vergnas who passed away on January 19, 2013 at age 72. Michel Las Vergnaswas a combinatorialmathematicianwith artistic sense and creativity. He is also well known as a cofounder of the theory of oriented matroids which acquired the firm acceptance as fundamental concept in mathematics. Michel was one of the founding editors of European Journal of Combinatorics. On personal side,Michel had broad and deep interest inmusic, arts and culture.Michel was a warm-hearted individual caring for his family and friends with kind and genuine smiles. Michel was the first doctoral student of another great combinatorialist Claude Berge. They were two of the leaders of the Paris school of combinatorics (L’Equipe Combinatoire, Université Paris VI). They influenced greatly the advances of combinatorial mathematics in the world and guided many excellent graduate students. Both Claude and Michel had unusual talents to formulate beautiful conjectures. Throughout his whole career as Directeur de Recherche au CNRS and professor of Université Paris VI (Pierre et Marie Curie), Michel’s devotion to combinatorial mathematics and to the guidance of doctoral students was extraordinary. The late Yahya Ould Hamidoune and the first editor Raul were the first doctoral students ofMichel, graduated in 1978 and 1979, respectively. The third editor Emeric was the last student who completed his study in 2002. Michel had supervised 15 doctoral students. He won the silver medal of the CNRS in 1985. On his pioneering research front, Michel gave many equivalent axiomatizations of oriented matroids in an extensive manuscript,1 which unfortunately has never been fully published. Michel’s theorem on single-element extensions2 of oriented matroids turned out to be crucial in constructing fascinating examples and in resolving degeneracy in the abstract combinatorial setting of optimization. Michel had strong interest in a wide range of combinatorics beyond the oriented

A Tutte polynomial inequality for lattice path matroids

Let

On the Möbius function of the locally finite poset associated with a numerical semigroup

M

Two-Generator Numerical Semigroups and Fermat and Mersenne Numbers

be a matroid without loops or coloops and let

Complete Kneser Transversals

T(M;x,y)

Detecting minors in matroids through triangles

be its Tutte polynomial. In 1999 Merino and Welsh conjectured that

Matroid Toric Ideals: Complete Intersection, Minors, and Minimal Systems of Generators

\max(T(M;2,0), T(M;0,2))\geq T(M;1,1)