Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Klaus Dohmen"'
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol 6, Iss 1 (2003)
We present a two-variable polynomial, which simultaneously generalizes the chromatic polynomial, the independence polynomial, and the matching polynomial of a graph. This new polynomial satisfies both an edge decomposition formula and a vertex decomp
Externí odkaz:
https://doaj.org/article/8a1db87d1d9c44ac9e7f759cfcb4b421
Autor:
Klaus Dohmen
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol 4, Iss 1 (2000)
Let (A v) v ∈ V be a finite family of sets. We establish an improved inclusion-exclusion identity for each closure operator on the power set of V having the unique base property. The result generalizes three improvements of the inclusion-exclusion
Externí odkaz:
https://doaj.org/article/60fadbcfd60c4e73a4b1c818f37bafd9
Autor:
Klaus Dohmen, Peter Tittmann
Publikováno v:
Discrete Mathematics. 310:1265-1268
We present a unified approach to an important subclass of Bonferroni-type inequalities by considering the so-called binomially bounded functions. Our main result associates with each binomially bounded function a Bonferroni-type inequality. By approp
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::04a8e3ea4592065993742cd7d01ae442
https://doi.org/10.1016/j.disc.2009.11.031
https://doi.org/10.1016/j.disc.2009.11.031
Autor:
Klaus Dohmen
Publikováno v:
Advances in Applied Mathematics. 28(2):272-277
In this paper, we show that any convex geometry (dual antimatroid) gives rise to a lace map and deduce some recent variants of the inclusion-exclusion principle from Zeilberger's abstract lace expansion.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0e3d95883930cfd79baead0f1cf21716
Autor:
Klaus Dohmen
Publikováno v:
SIAM Journal on Discrete Mathematics. 16:156-171
This paper establishes a connection between the theory of convex geometries, the principle of inclusion-exclusion, and the topological concept of an abstract tube. In particular, it is shown that convex geometries give rise to improved inclusion-excl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::310f0f2e7461ccc143cc4c918a18de18
https://doi.org/10.1137/s0895480101392630
https://doi.org/10.1137/s0895480101392630
Autor:
Klaus Dohmen, Martin Trinks
Publikováno v:
The Electronic Journal of Combinatorics. 21
We establish a broad generalization of Whitney's broken circuit theorem on the chromatic polynomial of a graph to sums of type $\sum_{A\subseteq S} f(A)$ where $S$ is a finite set and $f$ is a mapping from the power set of $S$ into an abelian group.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::09af4767404783898ae0f8708571d47f
https://doi.org/10.37236/4356
https://doi.org/10.37236/4356
Autor:
Klaus Dohmen
Publikováno v:
Graphs and Combinatorics. 17:607-610
We restate and reprove Narushima's principle of inclusion–exclusion on partition lattices in terms of abstract tubes. In this way, some new Bonferroni-like inequalities for partition lattices are obtained.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a04d2bf71299ec8fb8d252cac1965f0d
https://doi.org/10.1007/pl00007253
https://doi.org/10.1007/pl00007253
Autor:
Klaus Dohmen
Publikováno v:
European Journal of Combinatorics. 21(8):989-992
We investigate the number of proper λ -colourings of a hypergraph extending a given proper precolouring. We prove that this number agrees with a polynomial in λ for any sufficiently largeλ , and we establish a generalization of Whitney’s broken
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ed8fd5b95b4fd4d478c18c6d63ccf603
Autor:
Klaus Dohmen
Publikováno v:
Aequationes mathematicae. 60:108-115
We present a new variant of the sieve formula as well as new expansions for the Tutte polynomial and Crapo's beta invariant, where the number of terms is reduced by excluding terms that cancel. The key is a general result on sums of type $ \sum_{J\su
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4925deffe09ad980eb04f2be0c60af1d
https://doi.org/10.1007/s000100050139
https://doi.org/10.1007/s000100050139
Autor:
Klaus Dohmen
Publikováno v:
Archiv der Mathematik. 72:298-303
We present an improvement of the inclusion-exclusion principle in which the number of terms is reduced by predicted cancellation. The improvement generalizes a related result of Narushima as well as a graph-theoretic theorem of Whitney. Applications
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7321c9e736033ced2cbf09192648dd0f
https://doi.org/10.1007/s000130050336
https://doi.org/10.1007/s000130050336