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trace inequality ★★

Author(s):

Let $ A,B $ be positive semidefinite, by Jensen's inequality, it is easy to see $ [tr(A^s+B^s)]^{\frac{1}{s}}\leq [tr(A^r+B^r)]^{\frac{1}{r}} $, whenever $ s>r>0 $.

What about the $ tr(A^s+B^s)^{\frac{1}{s}}\leq tr(A^r+B^r)^{\frac{1}{r}} $, is it still valid?

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Chromatic Number of Common Graphs ★★

Author(s): Hatami; Hladký; Kráľ; Norine; Razborov

Question   Do common graphs have bounded chromatic number?

Keywords: common graph

Free DealDash Bids Cheats Bids Generator 2023-2024 ★★

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Free DealDash Bids Cheats Bids Generator 2023-2024

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5-local-tensions ★★

Author(s): DeVos

Conjecture   There exists a fixed constant $ c $ (probably $ c=4 $ suffices) so that every embedded (loopless) graph with edge-width $ \ge c $ has a 5-local-tension.

Keywords: coloring; surface; tension

Dense rational distance sets in the plane ★★★

Author(s): Ulam

Problem   Does there exist a dense set $ S \subseteq {\mathbb R}^2 $ so that all pairwise distances between points in $ S $ are rational?

Keywords: integral distance; rational distance

Unused Free Kim Kardashian Hollywood Cheats No Human Verification No Survey (2024 Method) ★★

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Unused Free Kim Kardashian Hollywood Cheats No Human Verification No Survey (2024 Method)

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Bingo Blitz Cheats Generator Unlimited No Jailbreak (Premium) ★★

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Bingo Blitz Cheats Generator Unlimited No Jailbreak (Premium)

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Oriented chromatic number of planar graphs ★★

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An oriented colouring of an oriented graph is assignment $ c $ of colours to the vertices such that no two arcs receive ordered pairs of colours $ (c_1,c_2) $ and $ (c_2,c_1) $. It is equivalent to a homomorphism of the digraph onto some tournament of order $ k $.

Problem   What is the maximal possible oriented chromatic number of an oriented planar graph?

Keywords: oriented coloring; oriented graph; planar graph

Family Island Cheats Generator 2024 No Human Verification (Real) ★★

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Family Island Cheats Generator 2024 No Human Verification (Real)

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Forcing a 2-regular minor ★★

Author(s): Reed; Wood

Conjecture   Every graph with average degree at least $ \frac{4}{3}t-2 $ contains every 2-regular graph on $ t $ vertices as a minor.

Keywords: minors

Beneš Conjecture ★★★

Author(s): Beneš

Let $ E $ be a non-empty finite set. Given a partition $ \bf h $ of $ E $, the stabilizer of $ \bf h $, denoted $ S(\bf h) $, is the group formed by all permutations of $ E $ preserving each block of $ \mathbf h $.

Problem  ($ \star $)   Find a sufficient condition for a sequence of partitions $ {\bf h}_1, \dots, {\bf h}_\ell $ of $ E $ to be complete, i.e. such that the product of their stabilizers $ S({\bf h}_1) S({\bf h}_2) \dots S({\bf h}_\ell) $ is equal to the whole symmetric group $ \frak S(E) $ on $ E $. In particular, what about completeness of the sequence $ \bf h,\delta(\bf h),\dots,\delta^{\ell-1}(\bf h) $, given a partition $ \bf h $ of $ E $ and a permutation $ \delta $ of $ E $?
Conjecture  (Beneš)   Let $ \bf u $ be a uniform partition of $ E $ and $ \varphi $ be a permutation of $ E $ such that $ \bf u\wedge\varphi(\bf u)=\bf 0 $. Suppose that the set $ \big(\varphi S({\bf u})\big)^{n} $ is transitive, for some integer $ n\ge2 $. Then $$ \frak S(E) = \big(\varphi S({\bf u})\big)^{2n-1}. $$

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Free Coin Master Cheats No Human Verification No Survey (2024 Method) ★★

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Free Coin Master Cheats No Human Verification No Survey (2024 Method)

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Sub-atomic product of funcoids is a categorical product ★★

Author(s):

Conjecture   In the category of continuous funcoids (defined similarly to the category of topological spaces) the following is a direct categorical product:
    \item Product morphism is defined similarly to the category of topological spaces. \item Product object is the sub-atomic product. \item Projections are sub-atomic projections.

See details, exact definitions, and attempted proofs here.

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Atomicity of the poset of multifuncoids ★★

Author(s): Porton

Conjecture   The poset of multifuncoids of the form $ (\mathscr{P}\mho)^n $ is for every sets $ \mho $ and $ n $:
    \item atomic; \item atomistic.

See below for definition of all concepts and symbols used to in this conjecture.

Refer to this Web site for the theory which I now attempt to generalize.

Keywords: multifuncoid

Chromatic number of associahedron ★★

Author(s): Fabila-Monroy; Flores-Penaloza; Huemer; Hurtado; Urrutia; Wood

Conjecture   Associahedra have unbounded chromatic number.

Keywords: associahedron, graph colouring, chromatic number

Shannon capacity of the seven-cycle ★★★

Author(s):

Problem   What is the Shannon capacity of $ C_7 $?

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Dragon Ball Legends Cheats Generator (Ios Android) ★★

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Dragon Ball Legends Cheats Generator (Ios Android)

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Multicolour Erdős--Hajnal Conjecture ★★★

Author(s): Erdos; Hajnal

Conjecture   For every fixed $ k\geq2 $ and fixed colouring $ \chi $ of $ E(K_k) $ with $ m $ colours, there exists $ \varepsilon>0 $ such that every colouring of the edges of $ K_n $ contains either $ k $ vertices whose edges are coloured according to $ \chi $ or $ n^\varepsilon $ vertices whose edges are coloured with at most $ m-1 $ colours.

Keywords: ramsey theory

Golf Battle Cheats Generator (Ios Android) ★★

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Golf Battle Cheats Generator (Ios Android)

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MONOPOLY GO Cheats Generator IOS Android No Verification 2024 (fresh method) ★★

Author(s):

MONOPOLY GO Cheats Generator IOS Android No Verification 2024 (fresh method)

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P vs. PSPACE ★★★

Author(s): Folklore

Problem   Is there a problem that can be computed by a Turing machine in polynomial space and unbounded time but not in polynomial time? More formally, does P = PSPACE?

Keywords: P; PSPACE; separation; unconditional

Fishdom Cheats Generator without verification (Free) ★★

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Fishdom Cheats Generator without verification (Free)

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2-colouring a graph without a monochromatic maximum clique ★★

Author(s): Hoang; McDiarmid

Conjecture   If $ G $ is a non-empty graph containing no induced odd cycle of length at least $ 5 $, then there is a $ 2 $-vertex colouring of $ G $ in which no maximum clique is monochromatic.

Keywords: maximum clique; Partitioning

Wall-Sun-Sun primes and Fibonacci divisibility ★★

Author(s):

Conjecture   For any prime $ p $, there exists a Fibonacci number divisible by $ p $ exactly once.

Equivalently:

Conjecture   For any prime $ p>5 $, $ p^2 $ does not divide $ F_{p-\left(\frac p5\right)} $ where $ \left(\frac mn\right) $ is the Legendre symbol.

Keywords: Fibonacci; prime

Simpsons Tapped Out Donuts Cash Cheats 2024 (Ios Android) ★★

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Simpsons Tapped Out Donuts Cash Cheats 2024 (Ios Android)

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MovieStarPlanet Generator Cheats 2024 (WORKING IN 5 SECOND) ★★

Author(s):

MovieStarPlanet Generator Cheats 2024 (WORKING IN 5 SECOND)

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Nearly spanning regular subgraphs ★★★

Author(s): Alon; Mubayi

Conjecture   For every $ \epsilon > 0 $ and every positive integer $ k $, there exists $ r_0 = r_0(\epsilon,k) $ so that every simple $ r $-regular graph $ G $ with $ r \ge r_0 $ has a $ k $-regular subgraph $ H $ with $ |V(H)| \ge (1- \epsilon) |V(G)| $.

Keywords: regular; subgraph

Decomposing a connected graph into paths. ★★★

Author(s): Gallai

Conjecture   Every simple connected graph on $ n $ vertices can be decomposed into at most $ \frac{1}{2}(n+1) $ paths.

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Weighted colouring of hexagonal graphs. ★★

Author(s): McDiarmid; Reed

Conjecture   There is an absolute constant $ c $ such that for every hexagonal graph $ G $ and vertex weighting $ p:V(G)\rightarrow \mathbb{N} $, $$\chi(G,p) \leq \frac{9}{8}\omega(G,p) + c $$

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The Sims Mobile Cheats Generator Free 2024 No Verification Android iOS (tips codes) ★★

Author(s):

The Sims Mobile Cheats Generator Free 2024 No Verification Android iOS (tips codes)

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Birch & Swinnerton-Dyer conjecture ★★★★

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Conjecture   Let $ E/K $ be an elliptic curve over a number field $ K $. Then the order of the zeros of its $ L $-function, $ L(E, s) $, at $ s = 1 $ is the Mordell-Weil rank of $ E(K) $.

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Decomposing eulerian graphs ★★★

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Conjecture   If $ G $ is a 6-edge-connected Eulerian graph and $ P $ is a 2-transition system for $ G $, then $ (G,P) $ has a compaible decomposition.

Keywords: cover; cycle; Eulerian

Working Generator Pokemon Go Pokecoins Cheats Android Ios 2024 (HOT) ★★

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Working Generator Pokemon Go Pokecoins Cheats Android Ios 2024 (HOT)

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My Singing Monsters Cheats Generator Android Ios 2024 Cheats Generator (re-designed) ★★

Author(s):

My Singing Monsters Cheats Generator Android Ios 2024 Cheats Generator (re-designed)

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A sextic counterexample to Euler's sum of powers conjecture ★★

Author(s): Euler

Problem   Find six positive integers $ x_1, x_2, \dots, x_6 $ such that $$x_1^6 + x_2^6 + x_3^6 + x_4^6 + x_5^6 = x_6^6$$ or prove that such integers do not exist.

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Hungry Shark Evolution Cheats Generator IOS Android No Survey 2024 (Generator!) ★★

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Hungry Shark Evolution Cheats Generator IOS Android No Survey 2024 (Generator!)

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Fasted Way! For Free Golf Battle Cheats Generator Working 2024 Android Ios ★★

Author(s):

Fasted Way! For Free Golf Battle Cheats Generator Working 2024 Android Ios

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Are all Fermat Numbers square-free? ★★★

Author(s):

Conjecture   Are all Fermat Numbers \[ F_n  = 2^{2^{n } }  + 1 \] Square-Free?

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Complexity of square-root sum ★★

Author(s): Goemans

Question   What is the complexity of the following problem?

Given $ a_1,\dots,a_n; k $, determine whether or not $  \sum_i \sqrt{a_i} \leq k.  $

Keywords: semi-definite programming

Criterion for boundedness of power series

Author(s): Rüdinger

Question   Give a necessary and sufficient criterion for the sequence $ (a_n) $ so that the power series $ \sum_{n=0}^{\infty} a_n x^n $ is bounded for all $ x \in \mathbb{R} $.

Keywords: boundedness; power series; real analysis

Every metamonovalued funcoid is monovalued ★★

Author(s): Porton

Conjecture   Every metamonovalued funcoid is monovalued.

The reverse is almost trivial: Every monovalued funcoid is metamonovalued.

Keywords: monovalued

Free Hollywood Story Free Diamonds Gems Cheats 2024 (Safe) ★★

Author(s):

Free Hollywood Story Free Diamonds Gems Cheats 2024 (Safe)

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Is Skewes' number e^e^e^79 an integer? ★★

Author(s):

Conjecture  

Skewes' number $ e^{e^{e^{79}}} $ is not an integer.

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Combinatorial covering designs

Author(s): Gordon; Mills; Rödl; Schönheim

A $ (v, k, t) $ covering design, or covering, is a family of $ k $-subsets, called blocks, chosen from a $ v $-set, such that each $ t $-subset is contained in at least one of the blocks. The number of blocks is the covering’s size, and the minimum size of such a covering is denoted by $ C(v, k, t) $.

Problem   Find a closed form, recurrence, or better bounds for $ C(v,k,t) $. Find a procedure for constructing minimal coverings.

Keywords: recreational mathematics

eFootball 2023 Cheats Generator Unlimited IOS Android No Survey 2024 (Reedem Today) ★★

Author(s):

eFootball 2023 Cheats Generator Unlimited IOS Android No Survey 2024 (Reedem Today)

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Algorithm for graph homomorphisms ★★

Author(s): Fomin; Heggernes; Kratsch

Question  

Is there an algorithm that decides, for input graphs $ G $ and $ H $, whether there exists a homomorphism from $ G $ to $ H $ in time $ O(c^{|V(G)|+|V(H)|}) $ for some constant $ c $?

Keywords: algorithm; Exponential-time algorithm; homomorphism

Free Idle Miner Tycoon Cheats Generator No Human Verification No Survey (Unused) ★★

Author(s):

Free Idle Miner Tycoon Cheats Generator No Human Verification No Survey (Unused)

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V-Bucks Generator Unlimited Generator (No Human Verification) ★★

Author(s):

V-Bucks Generator Unlimited Generator (No Human Verification)

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Giuga's Conjecture on Primality ★★

Author(s): Giuseppe Giuga

Conjecture   $ p $ is a prime iff $ ~\displaystyle \sum_{i=1}^{p-1} i^{p-1} \equiv -1 \pmod p $

Keywords: primality

Critical Ops Unlimited Credits Cheats IOS Android No Survey 2024 (Reedem Today) ★★

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Critical Ops Unlimited Credits Cheats IOS Android No Survey 2024 (Reedem Today)

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