A simple proof of Graham and Pollak's theorem
نویسندگان
چکیده
Graham and Pollak [Bell System Tech. J. 50 (1971) 2495–2519] obtained a beautiful formula on the determinant of distance matrices of trees, which is independent of the structure of the trees. In this paper we give a simple proof of Graham and Pollak’s result. © 2005 Elsevier Inc. All rights reserved.
منابع مشابه
Partial proof of Graham Higman's conjecture related to coset diagrams
Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...
متن کاملOn Tychonoff's type theorem via grills
Let ${X_{alpha}:alphainLambda}$ be a collection of topological spaces, and $mathcal {G}_{alpha}$ be a grill on $X_{alpha}$ for each $alphainLambda$. We consider Tychonoffrq{}s type Theorem for $X=prod_{alphainLambda}X_{alpha}$ via the above grills and a natural grill on $X$ related to these grills, and present a simple proof to this theorem. This immediately yields the classical theorem...
متن کاملA new proof for the Banach-Zarecki theorem: A light on integrability and continuity
To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...
متن کاملThe Basic Theorem and its Consequences
Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...
متن کاملAnother proof of Banaschewski's surjection theorem
We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 113 شماره
صفحات -
تاریخ انتشار 2006