共查询到20条相似文献,搜索用时 31 毫秒
1.
《Discrete Mathematics》2022,345(9):112945
The coinvariant algebra is a quotient of the polynomial ring whose algebraic properties are governed by the combinatorics of permutations of length n. A word over the positive integers is packed if whenever appears as a letter of w, so does . We introduce a quotient of which is governed by the combinatorics of packed words. We relate our quotient to the generalized coinvariant rings of Haglund, Rhoades, and Shimozono as well as the superspace coinvariant ring. 相似文献
2.
4.
5.
6.
《Discrete Mathematics》2022,345(8):112903
Graphs considered in this paper are finite, undirected and loopless, but we allow multiple edges. The point partition number is the least integer k for which G admits a coloring with k colors such that each color class induces a -degenerate subgraph of G. So is the chromatic number and is the point arboricity. The point partition number with was introduced by Lick and White. A graph G is called -critical if every proper subgraph H of G satisfies . In this paper we prove that if G is a -critical graph whose order satisfies , then G can be obtained from two non-empty disjoint subgraphs and by adding t edges between any pair of vertices with and . Based on this result we establish the minimum number of edges possible in a -critical graph G of order n and with , provided that and t is even. For the corresponding two results were obtained in 1963 by Tibor Gallai. 相似文献
7.
8.
9.
10.
《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
11.
12.
13.
14.
15.
16.
17.
《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
18.
《Journal of Functional Analysis》2023,284(9):109877
We prove an atomic type decomposition for the noncommutative martingale Hardy space for all by an explicit constructive method using algebraic atoms as building blocks. Using this elementary construction, we obtain a weak form of the atomic decomposition of for all , and provide a constructive proof of the atomic decomposition for which resolves a main problem on the subject left open for the last twelve years. We also study -atoms, and show that every -atom can be decomposed into a sum of -atoms; consequently, for every , the -atoms lead to the same atomic space for all . As applications, we obtain a characterization of the dual space of the noncommutative martingale Hardy space () as a noncommutative Lipschitz space via the weak form of the atomic decomposition. Our constructive method can also be applied to prove some sharp martingale inequalities. 相似文献
19.