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147 papers · 1 filter
On product Schur triples in the integers
Letícia Mattos, Domenico Mergoni Cecchelli, Olaf Parczyk
Schur's theorem states that in any -colouring of the set of integers there is a monochromatic solution to , provided is sufficiently large. Abbott and Wang stud…
A combinatorial characterization of binomial edge ideals
Davide Bolognini, Antonio Macchia, Giancarlo Rinaldo +1
Several algebraic properties of a binomial edge ideal can be interpreted in terms of combinatorial properties of its associated graph . In particular, the so-called cut se…
Celebrating Loday's Associahedron
Vincent Pilaud, Francisco Santos, Günter M. Ziegler
We survey Jean-Louis Loday's vertex description of the associahedron, and its far reaching influence in combinatorics, discrete geometry and algebra. We present in particular four…
The number of polyiamonds is supermultiplicative
Vuong Bui
While the number of polyominoes is known to be supermultiplicative by a simple concatenation argument, it is still unknown whether the same applies to polyiamonds. This article pro…
Weighted Ehrhart Theory: Extending Stanley's nonnegativity theorem
Esme Bajo, Robert Davis, Jesús A. De Loera +4
We generalize R. P. Stanley's celebrated theorem that the -polynomial of the Ehrhart series of a rational polytope has nonnegative coefficients and is monotone under contai…
A topological version of Hedetniemi's conjecture for equivariant spaces
Vuong Bui, Hamid Reza Daneshpajouh
A topological version of the famous Hedetniemi conjecture says: The mapping index of the Cartesian product of two -spaces is equal to the minimum of their $\mathbb Z/2…