Every totally real algebraic integer is a tree eigenvalue
نویسندگان
چکیده
منابع مشابه
Every totally real algebraic integer is a tree eigenvalue
Graph eigenvalues are examples of totally real algebraic integers, i.e. roots of real-rooted monic polynomials with integer coefficients. Conversely, the fact that every totally real algebraic integer occurs as an eigenvalue of some finite graph is a deep result, conjectured forty years ago by Hoffman, and proved seventeen years later by Estes. This short paper provides an independent and eleme...
متن کاملThe integer transfinite diameter of intervals and totally real algebraic integers
In this paper we build on some recent work of Amoroso, and Borwein and Erdélyi to derive upper and lower estimates for the integer transfinite diameter of small intervals + 03B4], is a fixed rational and 03B4 ~ 0. We also study functions g-, g, g+ associated with transfinite diameters of Farey intervals. Then we consider certain polynomials, which we call critical polynomials, associated to a g...
متن کاملTrace of totally positive algebraic integers and integer transfinite diameter
Explicit auxiliary functions can be used in the “Schur-SiegelSmyth trace problem”. In the previous works, these functions were constructed only with polynomials having all their roots positive. Here, we use several polynomials with complex roots, which are found with Wu’s algorithm, and we improve the known lower bounds for the absolute trace of totally positive algebraic integers. This improve...
متن کاملTotally Real Integral Points on a Plane Algebraic Curve
Michel LAURENT Abstract. Let F (X,Y ) = ∑m i=0 ∑n j=0 ai,jX iY j be an absolutely irreducible polynomial in Z[X,Y ]. Suppose that m ≥ 1, n ≥ 2 and that the polynomial ∑n j=0 am,jY j is reducible in Q[Y ], has n simple roots and an unique real root. Let L be a totally real number field and let (ξ, ζ) ∈ OL ×L be such that F (ξ, ζ) = 0. We give an upper bound for the absolute height H(ξ) which dep...
متن کاملEvery Connected Sum of Lens Spaces Is a Real Component of a Uniruled Algebraic Variety
Let M be a connected sum of finitely many lens spaces, and let N be a connected sum of finitely many copies of S × S. We show that there is a uniruled algebraic variety X such that the connected sum M#N of M and N is diffeomorphic to a connected component of the set of real points X(R) of X. In particular, any finite connected sum of lens spaces is diffeomorphic to a real component of a unirule...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2015
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2014.09.001