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  • 1.
    Björner, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Wachs, Michelle
    Welker, Volkmar
    ON SEQUENTIALLY COHEN-MACAULAY COMPLEXES AND POSETS2009In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 169, no 1, p. 295-316Article in journal (Refereed)
    Abstract [en]

    The classes of sequentially Cohen-Macaulay and sequentially homotopy Cohen-Macaulay complexes and posets are studied. First, some different versions of the definitions are discussed and the homotopy type is determined. Second, it is shown how various constructions, such as join, product and rank-selection preserve these properties. Third, a characterization of sequential Cohen-Macaulayness for posets is given. Finally, in an appendix we outline connections with ring-theory and survey some uses of sequential Cohen-Macaulayness in commutative algebra.

  • 2.
    Gustafsson, Björn
    et al.
    KTH, Superseded Departments, Mathematics.
    Putinar, M.
    Linear analysis of quadrature domains. II2000In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 119, p. 187-216Article in journal (Refereed)
    Abstract [en]

    The natural correspondence between bounded planar quadrature domains, in the terminology of Aharonov-Shapiro, and certain square matrices with a distinguished cyclic vector is further exploited. Two different cubature formulas on quadrature domains, that is the computation of the integral of a real polynomial, are presented. The minimal defining polynomial of a quadrature domain is decomposed uniquely into a linear combination of moduli squares of complex polynomials. The geometry of a canonical rational embedding of a quadrature domain into the projective complement of a real affine ball is also investigated. Explicit computations on order-two quadrature domains illustrate the main results.

  • 3.
    Kiessling, Jonas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Properties of cellular classes of chain complexes2012In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 191, no 1, p. 483-505Article in journal (Refereed)
    Abstract [en]

    In this paper we prove certain properties of cellular and acyclic classes of chain complexes of modules over a commutative Noetherian ring. In particular, we show that if X is finite and belongs to some cellular class C, then Σ nH nX also belongs to C, for every n.

  • 4. Kurlberg, Pär
    The distribution of spacings between quadratic residues, II2000In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 120, p. 205-224Article in journal (Refereed)
    Abstract [en]

    We study the distribution of spacings between squares in Z/QZ as the number of prime divisors of Q tends to infinity. In [3] Kurlberg and Rudnick proved that the spacing distribution for square free Q is Poissonian, this paper extends the result to arbitrary Q.

  • 5. Matousek, Jiri
    et al.
    Sedgwick, Eric
    Tancer, Martin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Charles University, Czech Republic.
    Wagner, Uli
    UNTANGLING TWO SYSTEMS OF NONCROSSING CURVES2016In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 212, no 1, p. 37-79Article in journal (Refereed)
    Abstract [en]

    We consider two systems (alpha(1), ... ,alpha(m)) and (beta(1), ... , beta(n)) of simple curves drawn on a compact two-dimensional surface M with boundary. Each alpha(i) and each beta(j) is either an arc meeting the boundary of M at its two endpoints, or a closed curve. The a, are pairwise disjoint except for possibly sharing endpoints, and similarly for the beta(j). We want to "untangle" the beta(j) from the alpha(i) by a self-homeomorphism of M; more precisely, we seek a homeomorphism phi: M -> M fixing the boundary of M pointwise such that the total number of crossings of the a, with the phi(beta(j)) is as small as possible. This problem is motivated by an application in the algorithmic theory of embeddings and 3 -manifolds. We prove that if M is planar, i.e., a sphere with h >= 0 boundary components ("holes"), then O(mn) crossings can be achieved (independently of h), which is asymptotically tight, as an easy lower bound shows. In general, for an arbitrary (orientable or nonorientable) surface M with h holes and of (orientable or nonorientable) genus g >= 0, we obtain an O((m + n)(4)) upper bound, again independent of h and g. The proofs rely, among other things, on a result concerning simultaneous planar drawings of graphs by Erten and Kobourov.

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