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Sökning: AMNE:(NATURVETENSKAP Matematik Diskret matematik) > (2010-2019)

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1.
  • Xia, Jiacheng, 1991 (författare)
  • Vector-valued Eisenstein series of congruence types and their products
  • 2019
  • Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. We consider this problem for vector-valued modular forms, establish the framework of congruence types and obtain the structure of the space of vector-valued Eisenstein series using tools from representation theory. Based on this development and historic results, we show that the space of vector-valued modular forms of certain weights and any congruence type can be spanned by the invariant vectors of that type tensor at most two Eisenstein series.
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2.
  • Andrén, Lina J., 1980- (författare)
  • On Latin squares and avoidable arrays
  • 2010
  • Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • This thesis consists of the four papers listed below and a survey of the research area. I Lina J. Andrén: Avoiding (m, m, m)-arrays of order n = 2k II Lina J. Andrén: Avoidability of random arrays III Lina J. Andr´en: Avoidability by Latin squares of arrays with even order IV Lina J. Andrén, Carl Johan Casselgren and Lars-Daniel Öhman: Avoiding arrays of odd order by Latin squares Papers I, III and IV are all concerned with a conjecture by Häggkvist saying that there is a constant c such that for any positive integer n, if m ≤ cn, then for every n × n array A of subsets of {1, . . . , n} such that no cell contains a set of size greater than m, and none of the elements 1, . . . , n belongs to more than m of the sets in any row or any column of A, there is a Latin square L on the symbols 1, . . . , n such that there is no cell in L that contains a symbol that belongs to the set in the corresponding cell of A. Such a Latin square is said to avoid A. In Paper I, the conjecture is proved in the special case of order n = 2k . Paper III improves on the techniques of Paper I, expanding the proof to cover all arrays of even order. Finally, in Paper IV, similar methods are used together with a recoloring theorem to prove the conjecture for all orders. Paper II considers another aspect of the problem by asking to what extent way a deterministic result concerning the existence of Latin squares that avoid certain arrays can be used when the sets in the array are assigned randomly.
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5.
  • Holmgren, Cecilia, 1984- (författare)
  • Novel Characteristics of Split Trees by use of Renewal Theory
  • 2012
  • Ingår i: Electronic Journal of Probability. - 1083-6489 .- 1083-6489. ; 17, s. 5-
  • Tidskriftsartikel (refereegranskat)abstract
    • We investigate characteristics of random split trees introduced by Devroye [SIAM J Comput 28, 409-432, 1998]; split trees include e. g., binary search trees, m-ary search trees, quadtrees, median of (2k + 1)-trees, simplex trees, tries and digital search trees. More precisely: We use renewal theory in the studies of split trees, and use this theory to prove several results about split trees. A split tree of cardinality n is constructed by distributing n balls (which often represent data) to a subset of nodes of an infinite tree. One of our main results is a relation between the deterministic number of balls n and the random number of nodes N. In [5] there is a central limit law for the depth of the last inserted ball so that most nodes are close to depth lnn/mu + O(root lnn), where mu is some constant depending on the type of split tree; we sharpen this result by finding an upper bound for the expected number of nodes with depths >= lnn/mu - ln(1/2+epsilon) n or depths <= lnn/mu + ln(1/2+epsilon) n for any choice of epsilon > 0. We also find the first asymptotic of the variances of the depths of the balls in the tree.
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6.
  • Holmgren, Cecilia, 1984- (författare)
  • Random Records and Cuttings in Binary Search Trees
  • 2010
  • Ingår i: Combinatorics, probability & computing. - 0963-5483 .- 1469-2163. ; 19:3, s. 391-424
  • Tidskriftsartikel (refereegranskat)abstract
    • We study the number of random records in a  binary search tree with n vertices (or equivalently, the number of cuttings required to eliminate the tree). We show that a classical limit theorem for convergence of sums of triangular arrays to infinitely divisible distributions can be used to determine the distribution of this number. The asymptotic distribution of the (normalized) number of records or cuts is found to be weakly 1-stable.
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7.
  • Uscka-Wehlou, Hania, 1973- (författare)
  • Continued fractions, Fibonacci numbers, and some classes of irrational numbers
  • 2010
  • Ingår i: Acta Mathematica Academiae Paedagogiace Nyíregyháziensis. - 1786-0091. ; 26:1, s. 17-30
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we define an equivalence relation on the set of positive irrational numbers less than 1. The relation is defined by means of continued fractions. Equivalence classes under this relation are determined by the places of some elements equal to 1 (called essential 1's) in the continued fraction expansion of numbers. Analysis of suprema of all equivalence classes leads to a solution which involves Fibonacci numbers and constitutes the main result of this paper. The problem has its origin in the author'sresearch on the construction of digital lines and upper and lower mechanical and characteristic words according to the hierarchy of runs.
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8.
  • Öhman, Lars-Daniel (författare)
  • Partial latin squares are avoidable
  • 2011
  • Ingår i: Annals of Combinatorics. - : Springer Science and Business Media LLC. - 0218-0006 .- 0219-3094. ; 15:3, s. 485-497
  • Tidskriftsartikel (refereegranskat)abstract
    • A square array is avoidable if for each set of n symbols there is an n x n Latin square on these symbols which differs from the array in every cell. The main result of this paper is that for m >= 2 any partial Latin square of order 4m - 1 is avoidable, thus concluding the proof that any partial Latin square of order at least 4 is avoidable.
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9.
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10.
  • Thunberg, Hans, 1956- (författare)
  • Tonsättaren Per Nörgårds ''oändlighetsserie"
  • 2013
  • Ingår i: Normat. - : Scandinavian University Press. - 0801-3500. ; 61:1, s. 33-47
  • Tidskriftsartikel (refereegranskat)abstract
    • This article presents a mathematical description, in terms of recursively defined number sequences, of the algorithms devised by the Danish composer Nørgård. The ambition of the latter was to generate from a very short sequence of tones melodies rich in symmetries and selfsimilarities, melodies which could be aperiodic and hence infinite in length. Given the mathematical presentation a variety of results can be formulated and proved. Note that the well-known Thue-Morse sequence is essentially a special case.
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