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  • 1.
    Alexandersson, Per
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Sawhney, Mehtaab
    MIT,USA.
    Properties of Non-symmetric Macdonald Polynomials at q=1 and q=02019Ingår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 23, nr 2, s. 219-239Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We examine the non-symmetric Macdonald polynomials E at q=1, as well as the more general permuted-basement Macdonald polynomials. When q=1, we show that E(x;1,t) is symmetric and independent of t whenever is a partition. Furthermore, we show that, in general , this expression factors into a symmetric and a non-symmetric part, where the symmetric part is independent of t, and the non-symmetric part only depends on x, t, and the relative order of the entries in . We also examine the case q=0, which gives rise to the so-called permuted-basement t-atoms. We prove expansion properties of these t-atoms, and, as a corollary, prove that Demazure characters (key polynomials) expand positively into permuted-basement atoms. This complements the result that permuted-basement atoms are atom-positive. Finally, we show that the product of a permuted-basement atom and a Schur polynomial is again positive in the same permuted-basement atom basis. Haglund, Luoto, Mason, and van Willigenburg previously proved this property for the identity basement and the reverse identity basement, so our result can be seen as an interpolation (in the Bruhat order) between these two results. The common theme in this project is the application of basement-permuting operators as well as combinatorics on fillings, by applying results in a previous article by Per Alexandersson.

  • 2. Backelin, Jörgen
    et al.
    Linusson, Svante
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Parity splits by triple point distances in X-trees2006Ingår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 10, nr 1, s. 1-18Artikel i tidskrift (Refereegranskat)
    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.

  • 3.
    Beck, Matthias
    et al.
    San Francisco State Univ, USA.
    Haase, Christian
    Free Univ Berlin, Germany.
    Higashitani, Akihiro
    Kyoto Sangyo Univ, Japan.
    Hofscheier, Johannes
    McMaster Univ, Canada.
    Jochemko, Katharina
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Katthan, Lukas
    Univ Minnesota, USA.
    Michalek, Mateusz
    Max Planck Inst Poland.
    Smooth Centrally Symmetric Polytopes in Dimension 3 are IDP2019Ingår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 23, nr 2, s. 255-262Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In 1997 Oda conjectured that every smooth lattice polytope has the integer decomposition property. We prove Oda's conjecture for centrally symmetric 3-dimensional polytopes, by showing they are covered by lattice parallelepipeds and unimodular simplices.

  • 4.
    Björner, Anders
    et al.
    KTH, Tidigare Institutioner, Matematik.
    Hultman, Axel
    KTH, Tidigare Institutioner, Matematik.
    A note on blockers in posets2004Ingår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 8, nr 2, s. 123-131Artikel i tidskrift (Refereegranskat)
    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.

  • 5. Eriksen, Niklas
    et al.
    Hultman, Axel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Expected reflection distance in G(r, 1, n) after a fixed number of reflections2005Ingår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 9, nr 1, s. 21-33Artikel i tidskrift (Refereegranskat)
    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.

  • 6.
    Eriksson, Henrik
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Eriksson, Kimmo
    Linusson, Svante
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Wästlund, Johan
    Dense packing of patterns in a permutation2007Ingår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 11, nr 3-4, s. 459-470Artikel i tidskrift (Refereegranskat)
    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.

  • 7.
    Incitti, Federico
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Permutation diagrams, fixed points and Kazhdan-Lusztig R-polynomials2006Ingår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 10, nr 3, s. 369-387Artikel i tidskrift (Refereegranskat)
    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.

  • 8. Johansson, Robert
    et al.
    Linusson, Svante
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Pattern avoidance in alternating sign matrices2007Ingår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 11, nr 04-mar, s. 471-480Artikel i tidskrift (Refereegranskat)
    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.

  • 9.
    Jonsson, Jakob
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    On the 3-Torsion Part of the Homology of the Chessboard Complex2010Ingår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 14, nr 4, s. 487-505Artikel i tidskrift (Refereegranskat)
    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.

  • 10.
    Liu, Fu
    et al.
    Univ Calif Davis, Dept Math, One Shields Ave, Davis, CA 95616 USA..
    Solus, Liam
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    On the Relationship Between Ehrhart Unimodality and Ehrhart Positivity2019Ingår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 23, nr 2, s. 347-365Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    For a given lattice polytope, two fundamental problems within the field of Ehrhart theory are (1) to determine if its (Ehrhart) h-polynomial is unimodal and (2) to determine if its Ehrhart polynomial has only positive coefficients. The former property of a lattice polytope is known as Ehrhart unimodality and the latter property is known as Ehrhart positivity. These two properties are often simultaneously conjectured to hold for interesting families of lattice polytopes, yet they are typically studied in parallel. As to answer a question posed at the 2017 Introductory Workshop to the MSRI Semester on Geometric and Topological Combinatorics, the purpose of this note is to show that there is no general implication between these two properties in any dimension greater than two. To do so, we investigate these two properties for families of well-studied lattice polytopes, assessing one property where previously only the other had been considered. Consequently, new examples of each phenomena are developed, some of which provide an answer to an open problem in the literature. The well-studied families of lattice polytopes considered include zonotopes, matroid polytopes, simplices of weighted projective spaces, empty lattice simplices, smooth polytopes, and s-lecture hall simplices.

  • 11.
    Norén, Patrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Engström, Alexander
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Ideals of graph homomorphisms2011Ingår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094Artikel i tidskrift (Övrigt vetenskapligt)
1 - 11 av 11
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