Smith Invariants and Dual Graded Graphs
نویسنده
چکیده
Abstract. The aim of this paper is to present evidence for a simple conjectural relation between eigenvalues and invariant factors of incidence matrices associated with adjacent ranks in differential posets. The conjectural relation yields the Smith invariants immediately, as the eigenvalues are completely understood [3, 15]. Furthermore, we consider more general structures: dual graded graphs [3]. In this setting, the aforementioned relations sometimes hold and other times fail. One particularly interesting example is the Young-Fibonacci lattice YF studied by Okada [14], which we show possesses the aforementioned conjectural relation.
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تاریخ انتشار 2007