| 61. |
- Uscka-Wehlou, Hanna, 1973-
(författare)
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Run-hierarchical structure of digital lines with irrational slopes in terms of continued fractions and the Gauss map
- 2009
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Ingår i: Pattern Recognition. - : Elsevier. - 0031-3203 .- 1873-5142. ; 42:10, s. 2247-2254
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Tidskriftsartikel (refereegranskat)abstract
- We study relations between digital lines and continued fractions. The main result is a parsimonious description of the construction of the digital line based only on the elements of the continued fraction representing its slope and containing only simple integer computations. The description reflects the hierarchy of digitization runs, which raises the possibility of dividing digital lines into equivalence classes depending on the continued fraction expansions of their slopes. Our work is confined to irrational slopes since, to our knowledge,there exists no such description for these, in contrast to rational slopes which have been extensively examined. The description is exact (it does not use approximations by rationals). Examples of lines with irrational slopes and with very simple digitization patterns are presented. These include both slopes with periodic and non-periodic continued fraction expansions, i.e.\ both quadratic surds and other irrationals. We also derive the connection between the Gauss map and the digitization parameters introduced by the author in 2007.
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| 62. |
- Uscka-Wehlou, Hanna, 1973-
(författare)
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Sturmian words with balanced construction
- 2009
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Ingår i: Proceedings of Words 2009, the 7th International Conference on Words (Salerno, Italy), 14--18 September 2009. - Italy : Salerno University.
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Konferensbidrag (refereegranskat)abstract
- In this paper we define Sturmian words with balanced construction. We formulate a fixed-point theorem for Sturmian words and analyze the set of all fixed points. The inspiration for this work came from the Kolakoski word and the general idea of self-reading sequences by P\u{a}un and Salomaa. The basis for this article is the author's earlier research on the influence of the continued fraction elements in the expansion of a positive irrational slope $a<1$ on the construction of runs for the upper mechanical word with slope $a$and intercept $0$.
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| 63. |
- Öhman, Lars-Daniel
(författare)
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Partial latin squares are avoidable
- 2011
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Ingår i: Annals of Combinatorics. - : Springer Science and Business Media LLC. - 0218-0006 .- 0219-3094. ; 15:3, s. 485-497
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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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| 64. |
- Arkeryd, Leif, 1940, et al.
(författare)
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Stationary solutions to the two-dimensional Broadwell model
- 2020
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Ingår i: Documenta Mathematica. - 1431-0643 .- 1431-0635. ; 25, s. 2023-2048
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Tidskriftsartikel (refereegranskat)abstract
- Existence of renormalized solutions to the two-dimensional stationary Broadwell model in a square with given indata in L-1 is proven. Averaging techniques from the continuous velocity case being unavailable when the velocities are discrete, the approach is based on direct L-1-compactness arguments using the Kolmogorov-Riesz theorem.
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| 65. |
- Brubaker, Ben, et al.
(författare)
-
Colored vertex models and Iwahori Whittaker functions
- 2024
-
Ingår i: Selecta Mathematica, New Series. - : Springer Nature. - 1420-9020 .- 1022-1824. ; 30:4
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Tidskriftsartikel (refereegranskat)abstract
- We give a recursive method for computing all values of a basis of Whittaker functions for unramified principal series invariant under an Iwahori or parahoric subgroup of a split reductive group G over a nonarchimedean local field F. Structures in the proof have surprising analogies to features of certain solvable lattice models. In the case G=GLr we show that there exist solvable lattice models whose partition functions give precisely all of these values. Here ‘solvable’ means that the models have a family of Yang–Baxter equations which imply, among other things, that their partition functions satisfy the same recursions as those for Iwahori or parahoric Whittaker functions. The R-matrices for these Yang–Baxter equations come from a Drinfeld twist of the quantum group Uq(gl^(r|1)), which we then connect to the standard intertwining operators on the unramified principal series. We use our results to connect Iwahori and parahoric Whittaker functions to variations of Macdonald polynomials.
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| 66. |
- Zhao, D., et al.
(författare)
-
Low Phase-Rank Approximation
- 2022
-
Ingår i: Linear Algebra and Its Applications. - : Elsevier BV. - 0024-3795. ; 639, s. 177-204
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we propose and solve low phase-rank approximation problems, which serve as a counterpart to the well-known low-rank approximation problem and the Schmidt-Mirsky theorem. It is well known that a nonzero complex number can be specified by its gain and phase, and while it is generally accepted that the gains of a matrix may be defined by its singular values, there is no widely accepted definition for its phases. In this work, we consider sectorial matrices, whose numerical ranges do not contain the origin, and adopt the canonical angles of such matrices as their phases. Similarly to the rank of a matrix being defined as the number of its nonzero singular values, we define the phase-rank of a sectorial matrix as the number of its nonzero phases. While a low-rank approximation problem is associated with the matrix arithmetic mean, it turns out that a natural parallel for the low phase-rank approximation problem is to use the matrix geometric mean to measure the approximation error. Importantly, we derive a majorization inequality between the phases of the geometric mean and the arithmetic mean of the phases, similarly to the Ky-Fan inequality for eigenvalues of Hermitian matrices. A characterization of the solutions to the proposed problem, with the same flavor as the Schmidt-Mirsky theorem, is then obtained in the case where both the objective matrix and the approximant are restricted to be positive-imaginary. In addition, we provide an alternative formulation of the low phase-rank approximation problem using geodesic distances between sectorial matrices. The two formulations give rise to the exact same set of solutions when the involved matrices are additionally assumed to be unitary. © 2022 Elsevier Inc.
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| 67. |
- Ardila, Federico, et al.
(författare)
-
The equivariant Ehrhart theory of the permutahedron
- 2020
-
Ingår i: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 148:12, s. 5091-5107
-
Tidskriftsartikel (refereegranskat)abstract
- Equivariant Ehrhart theory enumerates the lattice points in a polytope with respect to a group action. Answering a question of Stapledon, we describe the equivariant Ehrhart theory of the permutahedron, and we prove his Effectiveness Conjecture in this special case.
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| 68. |
- Eur, Christopher, et al.
(författare)
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The universal valuation of Coxeter matroids
- 2021
-
Ingår i: Bulletin of the London Mathematical Society. - : Wiley. - 0024-6093 .- 1469-2120. ; 53:3, s. 798-819
-
Tidskriftsartikel (refereegranskat)abstract
- Coxeter matroids generalize matroids just as flag varieties of Lie groups generalize Grassmannians. Valuations of Coxeter matroids are functions that behave well with respect to subdivisions of a Coxeter matroid into smaller ones. We compute the universal valuative invariant of Coxeter matroids. A key ingredient is the family of Coxeter Schubert matroids, which correspond to the Bruhat cells of flag varieties. In the process, we compute the universal valuation of generalized Coxeter permutohedra, a larger family of polyhedra that model Coxeter analogues of combinatorial objects such as matroids, clusters, and posets.
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| 69. |
- Lundman, Anders, 1985-, et al.
(författare)
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A note on higher order Gauss Maps
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We study Gauss maps of order k, associated to a projective variety X embedded in projective space via a line bundle L. We show that if X is a smooth, complete complex variety and L is a k-jet spanned line bundle on X, with k > 1, then the Gauss map of order k has finite fibers, unless X = P^n is embedded by the Veronese embedding of order k. In the case where X is a toric variety, we give a combinatorial description of the Gauss maps of order k, its image and the general fibers.
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| 70. |
- Lundman, Anders, 1985-
(författare)
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Computing Seshardi constants on smooth toric surfaces
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we compute the Seshadri constants at the general point on many smooth polarized toric surfaces. We consider the case when the degree of jet separation is small or the core of the associated polygon is a line segment. Our main result is that in this case the Seshadri constant at the general point can often be determined in terms of easily computable invariants of the surfaces at hand. Lastly we consider the case that the core of the associated polygon is a point for a smooth polarized toric surface (X, L ). We show that in this case X can be constructed via consecutive equivariant blow-ups of either P^2 or P^1 x P^1.
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