Relevant bibliographies by topics / Wilf’s conjecture

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Wilf’s conjecture'

Author: Grafiati
Published: 4 June 2021
Last updated: 12 February 2022

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Journal articles on the topic "Wilf’s conjecture"

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Bruns, Winfried, Pedro García-Sánchez, Christopher O’Neill, and Dane Wilburne. "Wilf’s conjecture in fixed multiplicity." International Journal of Algebra and Computation 30, no. 04 (March 13, 2020): 861–82. http://dx.doi.org/10.1142/s021819672050023x.

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We give an algorithm to determine whether Wilf’s conjecture holds for all numerical semigroups with a given multiplicity [Formula: see text], and use it to prove Wilf’s conjecture holds whenever [Formula: see text]. Our algorithm utilizes techniques from polyhedral geometry, and includes a parallelizable algorithm for enumerating the faces of any polyhedral cone up to orbits of an automorphism group. We also introduce a new method of verifying Wilf’s conjecture via a combinatorially flavored game played on the elements of a certain finite poset.
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Eliahou, Shalom. "Wilf’s conjecture and Macaulay’s theorem." Journal of the European Mathematical Society 20, no. 9 (June 6, 2018): 2105–29. http://dx.doi.org/10.4171/jems/807.

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Eliahou, Shalom, and Jean Fromentin. "Near-misses in Wilf’s conjecture." Semigroup Forum 98, no. 2 (February 20, 2018): 285–98. http://dx.doi.org/10.1007/s00233-018-9926-5.

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Angjelkoska, Violeta, and Donco Dimovski. "On a special case of Wilf’s conjecture." Asian-European Journal of Mathematics 13, no. 08 (May 28, 2020): 2050159. http://dx.doi.org/10.1142/s1793557120501594.

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Let [Formula: see text] be a numerical semigroup with embedding dimension [Formula: see text], minimal set of generators [Formula: see text], Frobenius number [Formula: see text], multiplicity [Formula: see text] and genus [Formula: see text]. In this paper, we prove that Wilfs conjecture i.e. the inequality [Formula: see text] holds for [Formula: see text] when [Formula: see text] is a basis for [Formula: see text]
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García-García, J. I., D. Marín-Aragón, and A. Vigneron-Tenorio. "An extension of Wilf’s conjecture to affine semigroups." Semigroup Forum 96, no. 2 (November 15, 2017): 396–408. http://dx.doi.org/10.1007/s00233-017-9906-1.

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Sammartano, Alessio. "Numerical semigroups with large embedding dimension satisfy Wilf’s conjecture." Semigroup Forum 85, no. 3 (January 4, 2012): 439–47. http://dx.doi.org/10.1007/s00233-011-9370-2.

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Cisto, Carmelo, Michael DiPasquale, Gioia Failla, Zachary Flores, Chris Peterson, and Rosanna Utano. "A generalization of Wilf’s conjecture for generalized numerical semigroups." Semigroup Forum 101, no. 2 (January 21, 2020): 303–25. http://dx.doi.org/10.1007/s00233-020-10085-7.

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Gu, Ze. "Compositions of a numerical semigroup." Discrete Mathematics and Applications 29, no. 5 (October 25, 2019): 345–50. http://dx.doi.org/10.1515/dma-2019-0032.

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Abstract Given a numerical semigroup S, a nonnegative integer a and m ∈ S ∖ {0}, we introduce the set C(S, a, m) = {s + aw(s mod m) | s ∈ S}, where {w(0), w(1), ⋯, w(m – 1)} is the Apéry set of m in S. In this paper we characterize the pairs (a, m) such that C(S, a, m) is a numerical semigroup. We study the principal invariants of C(S, a, m) which are given explicitly in terms of invariants of S. We also characterize the compositions C(S, a, m) that are symmetric, pseudo-symmetric and almost symmetric. Finally, a result about compliance to Wilf’s conjecture of C(S, a, m) is given.
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Brochard, Sylvain. "Proof of de Smit’s conjecture: a freeness criterion." Compositio Mathematica 153, no. 11 (August 14, 2017): 2310–17. http://dx.doi.org/10.1112/s0010437x17007370.

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Let $A\rightarrow B$ be a morphism of Artin local rings with the same embedding dimension. We prove that any $A$-flat $B$-module is $B$-flat. This freeness criterion was conjectured by de Smit in 1997 and improves Diamond’s criterion [The Taylor–Wiles construction and multiplicity one, Invent. Math. 128 (1997), 379–391, Theorem 2.1]. We also prove that if there is a nonzero $A$-flat $B$-module, then $A\rightarrow B$ is flat and is a relative complete intersection. Then we explain how this result allows one to simplify Wiles’s proof of Fermat’s last theorem: we do not need the so-called ‘Taylor–Wiles systems’ any more.
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Büyükboduk, Kâzim. "Stickelberger elements and Kolyvagin systems." Nagoya Mathematical Journal 203 (September 2011): 123–73. http://dx.doi.org/10.1017/s0027763000010345.

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AbstractIn this paper, we construct (many) Kolyvagin systems out of Stickelberger elements utilizing ideas borrowed from our previous work on Kolyvagin systems of Rubin-Stark elements. The applications of our approach are twofold. First, assuming Brumer’s conjecture, we prove results on the odd parts of the ideal class groups of CM fields which are abelian over a totally real field, and we deduce Iwasawa’s main conjecture for totally real fields (for totally odd characters). Although this portion of our results has already been established by Wiles unconditionally (and refined by Kurihara using an Euler system argument, when Wiles’s work is assumed), the approach here fits well in the general framework the author has developed elsewhere to understand Euler/Kolyvagin system machinery when the core Selmer rank isr >1 (in the sense of Mazur and Rubin). As our second application, we establish a rather curious link between the Stickelberger elements and Rubin-Stark elements by using the main constructions of this article hand in hand with the “rigidity” of the collection of Kolyvagin systems proved by Mazur, Rubin, and the author.
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Dissertations / Theses on the topic "Wilf’s conjecture"

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Dhayni, Mariam. "Problèmes dans la théorie des semigroupes numériques." Thesis, Angers, 2017. http://www.theses.fr/2017ANGE0041/document.

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Cette thèse est composée de deux parties. Nous étudions dans la première la conjecture de Wilf pour les semi-groupes numériques et la résolvons dans certains cas. Dans la seconde nous considérons une classe de semi-groupes presque arithmétiques et donnons pour ces semi-groupes des formules explicites pour la base d’Apéry, le nombre de Frobenius, et les nombres de pseudo-Frobenius. Nouscaractérisons aussi ceux qui sont symétriques (resp. pseudo-symétriques)
The thesis is made up of two parts. We study in the first part Wilf’s conjecture for numerical semigroups. We give an equivalent form of Wilf’s conjecture in terms of the Apéry set, embedding dimension and multiplicity of a numerical semigroup. We also give an affirmative answer for the conjecture in certain cases. In the second part, we consider a class of almost arithmetic numerical semigroups and give for this class of semigroups explicit formulas for the Apéry set, the Frobenius number, the genus and the pseudo-Frobenius numbers. We also characterize the symmetric (resp. pseudo-symmetric) numerical semigroups for this class of numerical semigroups
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Book chapters on the topic "Wilf’s conjecture"

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Amdeberhan, Tewodros, Valerio De Angelis, and Victor H. Moll. "Complementary Bell Numbers: Arithmetical Properties and Wilf’s Conjecture." In Advances in Combinatorics, 23–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-30979-3_2.

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Klazar, Martin. "The Füredi-Hajnal Conjecture Implies the Stanley-Wilf Conjecture." In Formal Power Series and Algebraic Combinatorics, 250–55. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04166-6_22.

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Delgado, Manuel. "Conjecture of Wilf: A Survey." In Numerical Semigroups, 39–62. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40822-0_4.

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Diamond, Fred, and Kenneth A. Ribet. "ℓ-adic Modular Deformations and Wiles’s “Main Conjecture”." In Modular Forms and Fermat’s Last Theorem, 357–73. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1974-3_12.

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Lubinsky, Doron S. "Reflections on the Baker–Gammel–Wills (Padé) Conjecture." In Analytic Number Theory, Approximation Theory, and Special Functions, 561–71. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-0258-3_21.

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Bras-Amorós, Maria, and César Marín Rodríguez. "New Eliahou Semigroups and Verification of the Wilf Conjecture for Genus up to 65." In Modeling Decisions for Artificial Intelligence, 17–27. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-85529-1_2.

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Wilson, Robin. "5. More triangles and squares." In Number Theory: A Very Short Introduction, 79–96. Oxford University Press, 2020. http://dx.doi.org/10.1093/actrade/9780198798095.003.0005.

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‘More triangles and squares’ explores Diophantine equations, named after the mathematician Diophantus of Alexandria. These are equations requiring whole number solutions. Which numbers can be written as the sum of two perfect squares? Joseph-Louis Lagrange’s theorem guarantees that every number can be written as the sum of four squares, and Edward Waring correctly suggested that there are similar results for higher powers. In 1637, Fermat conjectured that no three positive integers, a, b, and c, can satisfy the equation an+bn=cn, if n is greater than 2. Known as ‘Fermat’s last theorem’, this conjecture was eventually proved by Andrew Wiles in 1995.
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Journal articles
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