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71.
《Discrete Mathematics》2024,347(1):113658
Bent partitions are partitions of an elementary abelian group, which have similarities to partitions from spreads. In fact, a spread partition is a special case of a bent partition. In particular, bent partitions give rise to a large number of (vectorial) bent functions. Examples of bent partitions, which generalize the Desarguesian spread, have been presented by Anbar, Meidl and Pirsic, 2021, 2022. Bent partitions, which generalize some other classes of (pre)semifield spreads, have been presented by Anbar, Kalaycı, Meidl 2023. In this article, it is shown that these bent partitions induce -class amorphic associations schemes on , where k is a divisor of m with special properties. This implies a construction of amorphic association schemes from some classes of (pre)semifields. 相似文献
72.
In this note, we shall give a partition-theoretic interpretation which explains the non-negativity of the coefficients of some q-series arising from Ramanujan's Lost Notebook and prove the almost-increasingness of the coefficients via a vector partition generating function. 相似文献
73.
A n-vertex graph is said to be decomposable if, for any partition (λ1,…,λp) of the integer n, there exists a sequence (V1,…,Vp) of connected vertex-disjoint subgraphs with |Vi|=λi. The aim of the paper is to study the homeomorphism classes of decomposable trees. More precisely, we show that homeomorphism classes containing decomposable trees with an arbitrarily large minimal distance between all pairs of distinct vertices of degree different from 2, is exactly the set of combs. 相似文献
74.
Hansheng Diao 《Journal of Combinatorial Theory, Series A》2009,116(8):1361-1373
In this paper, we study partitions of positive integers into distinct quasifibonacci numbers. A digraph and poset structure is constructed on the set of such partitions. Furthermore, we discuss the symmetric and recursive relations between these posets. Finally, we prove a strong generalization of Robbins' result on the coefficients of a quasifibonacci power series. 相似文献
75.
Using Frobenius partitions we extend the main results of [4]. This leads to an infinite family of 4-way combinatorial identities. In some particular cases we get even 5-way combinatorial identities which give us four new combinatorial versions of Göllnitz-Gordon identities. 相似文献
76.
Nikita A. Nekrasov 《Japanese Journal of Mathematics》2009,4(1):63-93
We discuss instanton partition functions in various spacetime dimensions. These partition functions capture some information
about the spectrum of the supersymmetric gauge theories and their low-energy dynamics. Some of these theories can be defined
microscopically only through string theory. Remarkably, they even know about the M-theory. Our conjectures include the identities
between the generalization of the MacMahon formula and the character of M-theory, compactified down to 0 + 1 dimension.
This article is based on the 5th Takagi Lectures that the author delivered at the University of Tokyo on October 4 and 5,
2008. 相似文献
77.
For each rational number q=b/c where b≥c are positive integers, we define a q-brick of G to be a maximal subgraph H of G such that cH has b edge-disjoint spanning trees, and a q-superbrick of G to be a maximal subgraph H of G such that cH−e has b edge-disjoint spanning trees for all edges e of cH, where cH denotes the graph obtained from H by replacing each edge by c parallel edges. We show that the vertex sets of the q-bricks of G partition the vertex set of G, and that the vertex sets of the q-superbricks of G form a refinement of this partition. The special cases when q=1 are the partitions given by the connected components and the 2-edge-connected components of G, respectively. We obtain structural results on these partitions and describe their relationship to the principal partitions of a matroid. 相似文献
78.
Dániel Gerbner Nathan Lemons Dömötör Pálvölgyi Balázs Patkós 《Discrete Mathematics》2010,310(1):21-760
A general (rectangular) partition is a partition of a rectangle into an arbitrary number of non-overlapping subrectangles. This paper examines vertex 4-colorings of general partitions where every subrectangle is required to have all four colors appear on its boundary. It is shown that there exist general partitions that do not admit such a coloring. This answers a question of Dimitrov et al. [D. Dimitrov, E. Horev, R. Krakovski, Polychromatic colorings of rectangular partitions, Discrete Mathematics 309 (2009) 2957-2960]. It is also shown that the problem to determine if a given general partition has such a 4-coloring is NP-Complete. Some generalizations and related questions are also treated. 相似文献
79.
80.
Given a graph G=(V, E), let ${\mathcal{P}}$ be a partition of V. We say that ${\mathcal{P}}$ is dominating if, for each part P of ${\mathcal{P}}$, the set V\P is a dominating set in G (equivalently, if every vertex has a neighbor of a different part from its own). We say that ${\mathcal{P}}$ is acyclic if for any parts P, P′ of ${\mathcal{P}}$, the bipartite subgraph G[P, P′] consisting of the edges between P and P′ in ${\mathcal{P}}$ contains no cycles. The acyclic dominating number ad(G) of G is the least number of parts in any partition of V that is both acyclic and dominating; and we shall denote by ad(d) the maximum over all graphs G of maximum degree at most d of ad(G). In this article, we prove that ad(3)=2, which establishes a conjecture of P. Boiron, É. Sopena, and L. Vignal, DIMACS/DIMATIA Conference “Contemporary Trends in Discrete Mathematics”, 1997, pp. 1–10. For general d, we prove the upper bound ad(d)=O(dlnd) and a lower bound of ad(d)=Ω(d). © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 292–311, 2010 相似文献