Results 51 to 60 of about 28,564 (220)
Hodge theory in combinatorics [PDF]
, 2017 George Birkhoff proved in 1912 that the number of proper colorings of a finite graph G with n colors is a polynomial in n, called the chromatic polynomial of G.
M. Baker
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Properly Colored Cycles in Edge‐Colored Balanced Bipartite Graphs
Journal of Graph Theory, EarlyView.ABSTRACT Let G n , n c ${G}_{n,n}^{c}$ denote a (not necessarily properly) edge‐colored balanced bipartite graph on 2 n $2n$ vertices, that is, in which every edge is assigned a color. A cycle C $C$ in G n , n c ${G}_{n,n}^{c}$ is called properly colored if any two consecutive edges of C $C$ have distinct colors. A properly colored cycle‐factor of G n ,
Tingting Han +3 more
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Compatible cycles and CHY integrals
Journal of High Energy Physics, 2019 The CHY construction naturally associates a vector in ℝ(n−3)! to every 2- regular graph with n vertices. Partial amplitudes in the biadjoint scalar theory are given by the inner product of vectors associated with a pair of cycles.
Freddy Cachazo +2 more
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The generalized 3-connectivity of Lexicographic product graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Graph ...
Xueliang Li, Yaping Mao
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Creativity and Innovation Management, EarlyView.ABSTRACT This paper explores the limits of mission‐directed entrepreneurial states by drawing on the theory of recombinant innovation and F.A. Hayek's insights on the spontaneous growth of knowledge in society. First, the use of discretionary policymaking curtails the range of knowledge generated in the process of social interaction, limiting the scope
Bryan Cheang, Praharsh Mehrotra
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The Role of Dice in the Emergence of the Probability Calculus
International Statistical Review, EarlyView.Summary The early development of the probability calculus was clearly influenced by the roll of dice. However, while dice have been cast since time immemorial, documented calculations on the frequency of various dice throws date back only to the mid‐13th century.
David R. Bellhouse, Christian Genest
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The implications of generative artificial intelligence for mathematics education
School Science and Mathematics, EarlyView.Abstract Generative artificial intelligence has become prevalent in discussions of educational technology, particularly in the context of mathematics education. These AI models can engage in human‐like conversation and generate answers to complex questions in real‐time, with education reports accentuating their potential to make teachers' work more ...
Candace Walkington
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Extremal skew energy of digraphs with no even cycles [PDF]
Transactions on Combinatorics, 2014 Let $D$ be a digraph with skew-adjacency matrix $S(D)$. Then the skew energy of $D$ is defined to be the sum of the norms of all eigenvalues of $S(D)$. Denote by $mathcal{O}_n$ the class of digraphs on order $n$ with no even cycles, and by $mathcal{O ...
Jing Li, Xueliang Li, Huishu Lian
doaj
A note on global existence for boundary value problems
International Journal of Mathematics and Mathematical Sciences, 1989 Upper and lower solutions are used in establlsning global existence results for certain two–point boundary value problems for y‴=f(x,y,y′,y″) and y(n)=f(x,y,y′,...,y(n−1)).
Chuan J. Chyan, Johnny Henderson
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Coxeter-biCatalan combinatorics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We consider several counting problems related to Coxeter-Catalan combinatorics and conjecture that the problems all have the same answer, which we call the $W$ -biCatalan number. We prove the conjecture in many cases.
Emily Barnard, Nathan Reading
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