THEOREM OF THE DAY Sendov’s Conjecture (a Theorem Under Construction!) Let f (z) be a polynomial of degree n ≥ 2, all of whose zeros lie in the closed unit disk. Then for any zero z0 of f (z), the closed unit disk wi

Source URL: theoremoftheday.org

Around the Caccetta–Haggkvist Conjecture Andrzej Grzesik (Jagiellonian University) We will present some results and new approaches to the Caccetta– Haggkvist Conjecture and to the related problem — Seymour Second N

Source URL: web.mat.bham.ac.uk

Some problems related to the Tij conjecture. R. McCutcheon Let Tij be µ-preserving, commuting invertible transformations of X, i, j ∈ N. For finite γ ⊂ N × N, put

Source URL: fourier.math.uoc.gr

NONEXPANSIVE Z2 -SUBDYNAMICS AND NIVAT’S CONJECTURE VAN CYR AND BRYNA KRA Abstract. For a finite alphabet A and η : Z → A, the Morse-Hedlund Theorem states that η is periodic if and only if there exists n ∈ N suc

Source URL: www.facstaff.bucknell.edu

˝ CONJECTURE A REFINEMENT OF THE CAMERON-ERDOS ´ NOGA ALON, JOZSEF BALOGH, ROBERT MORRIS, AND WOJCIECH SAMOTIJ Abstract. In this paper we study sum-free subsets of the set {1, . . . , n}, that is, subsets of

Source URL: w3.impa.br

Kneser-Poulsen conjecture for large radii Igors Gorbovickis June 1, 2009 Abstract In this paper we prove the Kneser-Poulsen conjecture for large radii. Namely, if a finite number of points in Euclidean space E n is rearr

Source URL: www.cs.elte.hu

THEOREM OF THE DAY Kneser’s Conjecture Let Cn,k , 1 ≤ 2k − 1 ≤ n, denote the set of all k-element subsets of {1, . . . , n}. Let C1 ∪ . . . ∪ Ct = Cn,k , 1 ≤ t, be a partition of Cn,k such that any two sets

Source URL: www.theoremoftheday.org

NONEXPANSIVE Z2 -SUBDYNAMICS AND NIVAT’S CONJECTURE VAN CYR AND BRYNA KRA Abstract. For a finite alphabet A and η : Z → A, the Morse-Hedlund Theorem states that η is periodic if and only if there exists n ∈ N suc

Source URL: www.math.northwestern.edu

Congruent Numbers Kent E. Morrison Here are the first 10 congruent numbers along with the side lengths of the associated right triangles. n 5

Source URL: www.aimath.org

• Elliptic curves
• Number theory
• Triangle geometry
• Group theory
• Analytic number theory
• Congruent number
• Birch and Swinnerton-Dyer conjecture
• Heegner point
• Prime number
• Shape
• Heegner
• Bryan John Birch

THEOREM OF THE DAY Netto’s Conjecture (Dixon’s Theorem) The proportion of pairs of permutations of n elements which generate the whole symmetric group tends to 34 as n → ∞. Multiplying permutations is order-depen

Source URL: www.theoremoftheday.org