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Zhuang He 《Journal of Pure and Applied Algebra》2019,223(10):4426-4445
For every , we find a sufficient condition for the blow-up of a weighted projective space at the identity point not to be a Mori Dream Space. We exhibit several infinite sequences of weights satisfying this condition in all dimensions . 相似文献
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Let be the finite field of order q. Let G be one of the three groups , or and let W be the standard n-dimensional representation of G. For non-negative integers m and d we let denote the representation of G given by the direct sum of m vectors and d covectors. We exhibit a minimal set of homogeneous invariant polynomials such that for all cases except when and or . 相似文献
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《Discrete Mathematics》2022,345(10):113004
Let G be a graph. We say that G is perfectly divisible if for each induced subgraph H of G, can be partitioned into A and B such that is perfect and . We use and to denote a path and a cycle on t vertices, respectively. For two disjoint graphs and , we use to denote the graph with vertex set and edge set , and use to denote the graph with vertex set and edge set . In this paper, we prove that (i) -free graphs are perfectly divisible, (ii) if G is -free with , (iii) if G is -free, and (iv) if G is -free. 相似文献
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《Discrete Mathematics》2022,345(9):112977
Consider functions , where A and C are disjoint finite sets. The weakly connected components of the digraph of such a function are cycles of rooted trees, as in random mappings, and isolated rooted trees. Let and . When a function is chosen from all possibilities uniformly at random, then we find the following limiting behaviour as . If , then the size of the maximal mapping component goes to infinity almost surely; if , a constant, then process counting numbers of mapping components of different sizes converges; if , then the number of mapping components converges to 0 in probability. We get estimates on the size of the largest tree component which are of order when and constant when , . These results are similar to ones obtained previously for random injections, for which the weakly connected components are cycles and linear trees. 相似文献
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《Discrete Mathematics》2022,345(10):113001
The linked double star , where , is the graph consisting of the union of two stars and with a path on c vertices joining the centers. Its Ramsey number is the smallest integer r such that every 2-coloring of the edges of a admits a monochromatic . In this paper, we study the Ramsey numbers of linked double stars when c is odd. In particular, we establish bounds on the value of and determine the exact value of if , or if and . 相似文献
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