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    Article

    The square Frobenius number

    Let \(S=\left\langle s_1,\ldots ,s_n\right\rangle \) S = ...

    Jonathan Chappelon, Jorge Luis Ramírez Alfonsín in Semigroup Forum (2022)

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    Article

    Cubic Graphs, Their Ehrhart Quasi-Polynomials, and a Scissors Congruence Phenomenon

    The scissors congruence conjecture for the unimodular group is an analogue of Hilbert’s third problem, for the equidecomposability of polytopes. Liu and Osserman studied the Ehrhart quasi-polynomials of polyto...

    Cristina G. Fernandes, José C. de Pina… in Discrete & Computational Geometry (2021)

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    Article

    Counting Hamiltonian Cycles in the Matroid Basis Graph

    We present superfactorial and exponential lower bounds on the number of Hamiltonian cycles passing through any edge of the basis graph of generalized Catalan, uniform, and graphic matroids. All lower bounds we...

    Cristina G. Fernandes, César Hernández-Vélez, José C. de Pina… in Graphs and Combinatorics (2019)

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    Article

    On Lattice Path Matroid Polytopes: Integer Points and Ehrhart Polynomial

    In this paper we investigate the number of integer points lying in dilations of lattice path matroid polytopes. We give a characterization of such points as polygonal paths in the diagram of the lattice path m...

    Kolja Knauer, Leonardo Martínez-Sandoval… in Discrete & Computational Geometry (2018)

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    Article

    How Many Circuits Determine an Oriented Matroid?

    Las Vergnas and Hamidoune studied the number of circuits needed to determine an oriented matroid. In this paper we investigate this problem and some new variants, as well as their interpretation in particular ...

    Kolja Knauer, Luis Pedro Montejano, Jorge Luis Ramírez Alfonsín in Combinatorica (2018)

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    Article

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

    Let S be a numerical semigroup and let (ℤ,≤ S ) be the (locally finite) poset induced by S on the set of integers ℤ defined by x≤ S ...

    Jonathan Chappelon, Jorge Luis Ramírez Alfonsín in Semigroup Forum (2013)