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  • 1. Backelin, Jörgen
    et al.
    Linusson, Svante
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Parity splits by triple point distances in X-trees2006In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 10, no 1, p. 1-18Article in journal (Refereed)
    Abstract [en]

    At the conference Dress defined parity split maps by triple point distance and asked for a characterisation of such maps coming from binary phylogenetic X-trees. This article gives an answer to that question. The characterisation for X-trees can be easily described as follows: If all restrictions of a split map to sets of five or fewer elements is a parity split map for an X-tree, then so is the entire map. To ensure that the parity split map comes from an X-tree which is binary and phylogenetic, we add two more technical conditions also based on studying at most five points at a time.

  • 2.
    Björner, Anders
    et al.
    KTH, Superseded Departments, Mathematics.
    Hultman, Axel
    KTH, Superseded Departments, Mathematics.
    A note on blockers in posets2004In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 8, no 2, p. 123-131Article in journal (Refereed)
    Abstract [en]

    The blocker A* of an antichain A in a finite poset P is the set of elements minimal with the property of having with each member of A a common predecessor. The following is done: (1) The posets P for which A** = A for all antichains are characterized.(2) The blocker A* of a symmetric antichain in the partition lattice is characterized.(3) Connections with the question of finding minimal size blocking sets for certain set families are discussed.

  • 3. Eriksen, Niklas
    et al.
    Hultman, Axel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Expected reflection distance in G(r, 1, n) after a fixed number of reflections2005In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 9, no 1, p. 21-33Article in journal (Refereed)
    Abstract [en]

    Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G (r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G (r, 1, n) characters and on the eigenvalues of certain adjacency matrices.

  • 4.
    Eriksson, Henrik
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Eriksson, Kimmo
    Linusson, Svante
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Wästlund, Johan
    Dense packing of patterns in a permutation2007In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 11, no 3-4, p. 459-470Article in journal (Refereed)
    Abstract [en]

    We study the length L-k of the shortest permutation containing all patterns of length k. We establish the bounds e(-2)k(2) < L-k <= (2/3 + o(1))k(2). We also prove that as k there are permutations of length (1/4+o(1))k(2) containing almost all patterns of length k.

  • 5.
    Incitti, Federico
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Permutation diagrams, fixed points and Kazhdan-Lusztig R-polynomials2006In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 10, no 3, p. 369-387Article in journal (Refereed)
    Abstract [en]

    In this paper, we give an algorithm for computing the Kazhdan-Lusztig R-polynomials in the symmetric group. The algorithm is described in terms of permutation diagrams. In particular we focus on how the computation of the polynomial is affected by certain fixed points. As a consequence of our methods, we obtain explicit formulas for the R-polynomials associated with some general classes of intervals, generalizing results of Brenti and Pagliacci.

  • 6. Johansson, Robert
    et al.
    Linusson, Svante
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Pattern avoidance in alternating sign matrices2007In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 11, no 04-mar, p. 471-480Article in journal (Refereed)
    Abstract [en]

    We generalize the definition of a pattern from permutations to alternating sign matrices. The number of alternating sign matrices avoiding 132 is proved to be counted by the large Schroder numbers, 1, 2, 6, 22, 90, 394,.... We give a bijection between 132-avoiding alternating sign matrices and Schroder paths, which gives a refined enumeration. We also show that the 132-, 123-avoiding alternating sign matrices are counted by every second Fibonacci number.

  • 7.
    Jonsson, Jakob
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On the 3-Torsion Part of the Homology of the Chessboard Complex2010In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 14, no 4, p. 487-505Article in journal (Refereed)
    Abstract [en]

    Let 1 (d) (M-m,M-n; Z) not equal 0. Second, for each k >= 0, we show that there is a polynomial f(k)(a, b) of degree 3k such that the dimension of (H) over tilde (k+a+2b-2) (M-k+a+3b-1,M- k+2a+3b-1; Z(3)), viewed as a vector space over Z(3), is at most f(k)(a, b) for all a >= 0 and b >= k+ 2. Third, we give a computer- free proof that (H) over tilde (2) (M-5,M-5; Z) congruent to Z(3). Several proofs are based on a new long exact sequence relating the homology of a certain subcomplex of M-m,M-n to the homology of M-m-2,M-n-1 and M-m-2,M-n-3.

  • 8.
    Norén, Patrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Engström, Alexander
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Ideals of graph homomorphisms2011In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094Article in journal (Other academic)
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