Staircase convex results for a certain class of orthogonal polytopes
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| 024 | 7 | 0 | |a 10.1007/s00010-014-0294-2 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0294-2 | ||
| 100 | 1 | |a Breen |D Marilyn |u The University of Oklahoma, OK, 73019, Norman, USA |4 aut | |
| 245 | 1 | 0 | |a Staircase convex results for a certain class of orthogonal polytopes |h [Elektronische Daten] |c [Marilyn Breen] |
| 520 | 3 | |a Let $${\mathcal{C}}$$ C be a finite family of distinct boxes in $${\mathbb{R}^{d}}$$ R d whose intersection graph is a block graph, and let $${S = \cup \{C :C {\rm in} \mathcal{C}\}}$$ S = ∪ { C : C in C } . Let $${T \subseteq S}$$ T ⊆ S . If for every a, b in T there is an a − b staircase in S, then T lies in a staircase convex union of boxes $${\cup \{B : B {\rm in} \mathcal{B}\}}$$ ∪ { B : B in B } , where each B i in $${\mathcal{B}}$$ B is a subset of some associated box C i in $${\mathcal{C}}$$ C and where the intersection graph of $${\mathcal{B}}$$ B is a connected block graph. This result, in turn, allows us to obtain for set S analogues of established theorems concerning staircase convex sets and their unions in $${\mathbb{R}^{d}}$$ R d . Moreover, when S is staircase starshaped, then its staircase kernel will be staircase convex. | |
| 540 | |a Springer Basel, 2014 | ||
| 690 | 7 | |a Orthogonal polytopes |2 nationallicence | |
| 690 | 7 | |a staircase convex sets |2 nationallicence | |
| 690 | 7 | |a staircase starshaped sets |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/4(2015-08-01), 1213-1221 |x 0001-9054 |q 89:4<1213 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0294-2 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-014-0294-2 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Breen |D Marilyn |u The University of Oklahoma, OK, 73019, Norman, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/4(2015-08-01), 1213-1221 |x 0001-9054 |q 89:4<1213 |1 2015 |2 89 |o 10 | ||