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Related papers: Chern Numbers of Matroids

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We settle the negativity conjecture of Vasconcelos for the Chern number of an ideal in certain unmixed quotients of regular local rings by explicit calculation of the Hilbert polynomials of all ideals generated by systems of parameters.

Commutative Algebra · Mathematics 2009-06-05 Mousumi Mandal , J. K. Verma

There is an explicit formula expressing the Chern-Schwartz-MacPherson class of a hypersurface in a nonsingular variety (in characteristic $0$) in terms of the Segre class of its jacobian subscheme; this has been known for a number of years.…

Algebraic Geometry · Mathematics 2019-10-30 Paolo Aluffi

We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a regular (aperiodic and irreducible) finite Markov chain. Specially, consider a random walk on a regular Markov chain and a Hermitian matrix-valued…

Machine Learning · Statistics 2020-10-30 Jiezhong Qiu , Chi Wang , Ben Liao , Richard Peng , Jie Tang

As an important figure of merit for characterizing the quantized collective behaviors of the wavefunction, Chern number is the topological invariant of quantum Hall insulators. Chern number also identifies the topological properties of the…

A theorem of Batyrev's asserts that if two nonsingular varieties V,W are birational, and their canonical bundles agree after pull-back to a resolution of indeterminacies of a birational map between them, then the Betti numbers of V and W…

Algebraic Geometry · Mathematics 2012-04-10 Paolo Aluffi

The cycles of a graph give a natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges are adjacent in one cycle if and only if they are adjacent in every cycle in which they appear together. An…

Combinatorics · Mathematics 2023-04-11 Cameron Crenshaw , James Oxley

We study an one-dimensional transverse field Ising model with additional periodically modulated real and complex fields. It is shown that both models can be mapped on a pseudo spin system in the k space in the aid of an extended Bogoliubov…

Quantum Physics · Physics 2016-11-17 C. Li , G. Zhang , Z. Song

The Chern number, as a topological invariant, characterizes the topological features of a 2D system and can be experimentally detected through Hall conductivity. In this work, we investigate the connection between the Chern number and the…

Quantum Physics · Physics 2024-10-29 D. K. He , Y. B. Shi , Z. Song

In this paper, we give a new axioms system based on nonseparable flats with their ranks to define a matroid. We deduce a polynomial time algorithm for deciding if a given matroid (respectively, arbitrary structure) is an uniform matroid.…

Combinatorics · Mathematics 2024-02-15 Brahim Chaourar

In this paper we construct a bivariant Chern character defined on ``families of spectral triples''. Such families should be viewed as a version of unbounded Kasparov bimodules adapted to the category of bornological algebras. The Chern…

Mathematical Physics · Physics 2009-11-07 Denis Perrot

An odd index theorem for higher odd Chern characters of crossed product algebras is proved. It generalizes the Noether-Gohberg-Krein index theorem. Furthermore, a local formula for the associated cyclic cocycle is provided. When applied to…

Mathematical Physics · Physics 2016-10-27 Emil Prodan , Hermann Schulz-Baldes

B\'ar\'any, Kalai, and Meshulam recently obtained a topological Tverberg-type theorem for matroids, which guarantees multiple coincidences for continuous maps from a matroid complex to d-dimensional Euclidean space, if the matroid has…

Combinatorics · Mathematics 2017-05-11 Pavle V. M. Blagojević , Albert Haase , Günter M. Ziegler

The set of the first Hilbert coefficients of parameter ideals relative to a module--its Chern coefficients--over a local Noetherian ring codes for considerable information about its structure--noteworthy properties such as that of…

Commutative Algebra · Mathematics 2014-04-03 Laura Ghezzi , Shiro Goto , Jooyoun Hong , Kazuho Ozeki , Tran Phuong , Wolmer Vasconcelos

Graphings serve as limit objects for bounded-degree graphs. We define the ``cycle matroid'' of a graphing as a submodular setfunction, with values in [0,1], which generalizes (up to normalization) the cycle matroid of finite graphs. We…

Combinatorics · Mathematics 2023-11-08 László Lovász

We apply Weiss calculus to compute the number of topological complex vector bundles of rank $n-2$ with vanishing Chern classes over $\mathbb{C}P^n$ for $n>3$, as given by the list $1, 1, 12, 2, 1, 3, 2, 2, 3, 1, 4, 6, 1, 1, 6, 2, 1, 3, 4,…

Algebraic Topology · Mathematics 2022-02-25 Yang Hu

We present a new direct proof of a topological representation theorem for oriented matroids in the general rank case. Our proof is based on an earlier rank 3 version. It uses hyperline sequences and the generalized Sch{\"o}nflies theorem.…

Combinatorics · Mathematics 2007-05-23 Juergen Bokowski , Simon King , Susanne Mock , Ileana Streinu

In this paper we prove that, at least in even complex dimensions, the ratio of Chern numbers for a closed complex hyperbolic branched cover manifold are not all equal to the corresponding ratio of Chern numbers for a closed complex…

Differential Geometry · Mathematics 2025-05-26 Barry Minemyer

By the work of Ferroni and Larson, Kazhdan-Lusztig polynomials and Z-polynomials of complete graphs have combinatorial interpretations in terms of quasi series-parallel matroids. We provide explicit formulas for the number of…

Combinatorics · Mathematics 2024-10-18 Nicholas Proudfoot , Yuan Xu , Ben Young

A class of matrix models which arises as partition function in U(N) Chern-Simons matter theories on three sphere is investigated. Employing the standard technique of the 1/N expansion we solve the system beyond the planar limit. In…

High Energy Physics - Theory · Physics 2019-12-06 Shuichi Yokoyama

We propose to use generic Chern numbers for a characterization of topological insulators. It is suitable for a numerical characterization of low dimensional quantum liquids where strong quantum fluctuations prevent from developing…

Strongly Correlated Electrons · Physics 2009-11-10 Yasuhiro Hatsugai