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Whitney numbers of partial dowling lattices | ||
Transactions on Combinatorics | ||
مقاله 7، دوره 13، شماره 2، شهریور 2024، صفحه 169-178 اصل مقاله (452.14 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2023.135127.2013 | ||
نویسنده | ||
Thomas Zaslavsky* | ||
Binghamton University, Binghamton, NY 13902-6000, U.S.A. | ||
چکیده | ||
The Dowling lattice $Q_n(G)$, $G$ a finite group, generalizes the geometric lattice generated by all vectors, over a field, with at most two nonzero components. Abstractly, it is a fundamental object in the classification of finite matroids. Constructively, it is the frame matroid of a certain gain graph known as $G K{_n}{^V}$. Its Whitney numbers of the first kind enter into several important formulas. Ravagnani suggested and partially proved that these numbers of $Q_n(G)$ and higher-weight generalizations are polynomial functions of $|G|$. We give a simple proof for $Q_n(G)$ and its generalization to a wider class of gain graphs and biased graphs, and we determine the degrees and coefficients of the polynomials. | ||
کلیدواژهها | ||
Matroid؛ Whitney number؛ Dowling lattice؛ group expansion gain graph | ||
مراجع | ||
[1] T. A. Dowling, A class of geometric lattices based on finite groups, J. Combin. Theory Ser. B, 14 (1973) 61–86. | ||
آمار تعداد مشاهده مقاله: 91 تعداد دریافت فایل اصل مقاله: 202 |