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  • 1.
    Alexandersson, Per
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Polytopes and Large Counterexamples2019Ingår i: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 28, nr 1, s. 115-120Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this short note, we give large counterexamples to natural questions about certain order polytopes, in particular, Gelfand–Tsetlin polytopes. Several of the counterexamples are too large to be discovered via a brute-force computer search. We also show that the multiset of hooks in a Young diagram is not enough information to determine the Ehrhart polynomial for an associated order polytope. This is somewhat counter-intuitive to the fact that the multiset of hooks always determine the leading coefficient of the Ehrhart polynomial.

  • 2. Amerik, Ekaterina
    et al.
    Kurlberg, Pär
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Nguyen, Khoa D.
    Towsley, Adam
    Viray, Bianca
    Voloch, Jose Felipe
    Evidence for the Dynamical Brauer-Manin Criterion2016Ingår i: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 25, nr 1, s. 54-65Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let phi: X -> X be a morphism of a variety over a number field K. We consider local conditions and a "Brauer-Manin" condition, defined by Hsia and Silverman, for the orbit of a point P is an element of X(K) to be disjoint from a subvariety V subset of X, i.e., for V boolean AND O-phi (P) = empty set. We provide evidence that the dynamical Brauer-Manin condition is sufficient to explain the lack of points in the intersection V boolean AND O-phi (P); this evidence stems from a probabilistic argument as well as unconditional results in the case of etale maps.

  • 3.
    Björner, Anders.
    et al.
    KTH, Tidigare Institutioner                               , Matematik.
    Lutz, F. H.
    Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincare homology 3-sphere2000Ingår i: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 9, nr 2, s. 275-289Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present a computer program based on bistellar operations that provides a useful too I for the construction of simplicial manifolds with few vertices. As an example, we obtain a 16-vertex triangulation of the Poincare homology 3-sphere; we construct an infinite series of non-FL d-dimensional spheres with d + 13 vertices for d greater than or equal to 5; and we show that ifa d-manifold, with d greater than or equal to 5, admits any triangulation on n vertices, it admits a noncombinatorial triangulation on n + 12 vertices.

  • 4. Brzezinski, J.
    et al.
    Holsztynski, W.
    Kurlberg, Pär
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    On the congruence ax plus by 1 modulo xy2005Ingår i: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 14, nr 4, s. 391-401Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We give bounds on the number of solutions to the Diophantine equation (X + 1/x)(Y + 1/y) = n as n tends to infinity. These bounds are related to the number of solutions to congruences of the form ax + by equivalent to 1 modulo xy.

  • 5.
    Engström, Alexander
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Discrete Morse Functions from Fourier Transforms2009Ingår i: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 18, nr 1, s. 45-53Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A discrete Morse function on a simplicial complex describes how to construct a homotopy-equivalent CW-complex with possibly fewer cells. We associate a Boolean function with a given simplicial complex and construct a discrete Morse function using its Fourier transform. Methods from theoretical computer science by O'Donnell, Saks, Schramm, and Servedio, together with experimental data on complexes from Hachimori's library and on chessboard complexes, provide some evidence that the constructed discrete Morse functions are efficient.

  • 6.
    Gaidashev, Denis
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Yampolsky, Michael
    Cylinder renormalization of siegel disks2007Ingår i: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 16, nr 2, s. 215-226Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study one of the central open questions in one-dimensional renormalization theory-the conjectural universality of golden-mean Siegel disks. We present an approach to the problem based on cylinder renormalization proposed by the second author. Numerical implementation of this approach relies on the constructive measurable Riemann mapping theorem proved by the first author. Our numerical study yields convincing evidence to support the hyperbolicity conjecture in this setting.

  • 7.
    Jonsson, Jakob
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    More Torsion in the Homology of the Matching Complex2010Ingår i: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 19, nr 3, s. 363-383Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A matching on a set X is a collection of pairwise disjoint subsets of X of size two Using computers, we analyze the integral homology of the matching complex M, which is the simplicial complex of matchings on the set {1, ,n} The main result is the detection of elements of order p in the homology for p is an element of {5, 7, 11, 13} Specifically, we show that there are elements of order 5 in the homology of M-n for n >= 18 and for n is an element of {14, 16} The only previously known value was n = 14, and in this particular case we have a new computer-free proof Moreover, we show that there are elements of order 7 in the homology of M-n for all odd a between 23 and 41 and for n = 30 In addition, there are elements of order 11 in the homology of M-47 and elements of order 13 in the homology of M-62 Finally, we compute the ranks of the Sylow 3- and 5-subgroups of the torsion part of (H) over tilde (d)(M-n, Z) for 13 <= n <= 16, a complete description of the homology already exists for n <= 12 To prove the results, we use a representation-theoretic approach, examining subcomplexes of the chain complex of M-n obtained by letting certain groups act on the chain complex.

  • 8.
    Lundow, Per Håkan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Kondenserade materiens teori.
    Markstrom, K.
    Broken-cycle-free subgraphs and the log-concavity conjecture for chromatic polynomials2006Ingår i: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 15, nr 3, s. 343-353Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper concerns the coefficients of the chromatic polynomial of a graph. We first report on a computational verification of the strict log-concavity conjecture for chromatic polynomials for all graphs on at most 11 vertices, as well as for certain cubic graphs. In the second part of the paper we give a number of conjectures and theorems regarding the behavior of the coefficients of the chromatic polynomial, in part motivated by our computations. Here our focus is on epsilon(G), the average size of a broken-cycle-free subgraph of the graph G, whose behavior under edge deletion and contraction is studied.

  • 9.
    Thunberg, Hans
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Feigenbaum Numbers for Certain Flat-Top Families1994Ingår i: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 3, nr 1, s. 51-57Artikel i tidskrift (Refereegranskat)
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