Log-concavity of the genus polynomials of Ringel Ladders
| Main Authors: | Gross, Jonathan L; Columbia University, Mansour, Toufik; Department of Mathematics, University of Haifa, 3498838 Haifa, Israel, Tucker, Thomas W.; Departments of Mathematics, Colgate University, Hamilton, NY 13346, USA, Wang, David G.L.; School of Mathematics and Statistics, Beijing Institute of Technology, 102488, P.R. China |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2015
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| Subjects: | |
| Online Access: |
http://www.ejgta.org/index.php/ejgta/article/view/92 http://www.ejgta.org/index.php/ejgta/article/view/92/pdf_3 |
Daftar Isi:
- A Ringel ladder can be formed by a self-bar-amalgamation operation on a symmetric ladder, that is, by joining the root vertices on its end-rungs. The present authors have previously derived criteria under which linear chains of copies of one or more graphs have log-concave genus polyno- mials. Herein we establish Ringel ladders as the first significant non-linear infinite family of graphs known to have log-concave genus polynomials. We construct an algebraic representation of self-bar-amalgamation as a matrix operation, to be applied to a vector representation of the partitioned genus distribution of a symmetric ladder. Analysis of the resulting genus polynomial involves the use of Chebyshev polynomials. This paper continues our quest to affirm the quarter-century-old conjecture that all graphs have log-concave genus polynomials.