Results 11 to 20 of about 22,632 (241)
Hilbert–Poincaré series of matroid Chow rings and intersection cohomology [PDF]
Advances in Mathematics, 2022 We study the Hilbert series of four objects arising in the Chow-theoretic and Kazhdan-Lusztig framework of matroids. These are, respectively, the Hilbert series of the Chow ring, the augmented Chow ring, the intersection cohomology module, and its stalk ...
L. Ferroni +3 more
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Truthful and Fair Mechanisms for Matroid-Rank Valuations [PDF]
AAAI Conference on Artificial Intelligence, 2021 We study the problem of allocating indivisible goods among strategic agents. We focus on settings wherein monetary transfers are not available and each agent's private valuation is a submodular function with binary marginals, i.e., the agents' valuations
Siddharth Barman, Paritosh Verma
semanticscholar +1 more source
A semi-small decomposition of the Chow ring of a matroid [PDF]
Advances in Mathematics, 2020 We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The decomposition is used to give simple proofs of Poincare duality, the hard Lefschetz theorem, and the Hodge-Riemann relations for the Chow ring, recovering the main result ...
Tom Braden +4 more
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Finding Fair and Efficient Allocations for Matroid Rank Valuations [PDF]
Algorithmic Game Theory, 2020 In this article, we present new results on the fair and efficient allocation of indivisible goods to agents whose preferences correspond to matroid rank functions.
Nawal Benabbou +3 more
semanticscholar +1 more source
On Fair Division under Heterogeneous Matroid Constraints [PDF]
AAAI Conference on Artificial Intelligence, 2020 We study fair allocation of indivisible goods among additive agents with feasibility constraints. In these settings, every agent is restricted to get a bundle among a specified set of feasible bundles.
Amitay Dror +2 more
semanticscholar +1 more source
Log-concavity of matroid h-vectors and mixed Eulerian numbers [PDF]
Duke mathematical journal, 2020 For any matroid $M$, we compute the Tutte polynomial $T_M(x,y)$ using the mixed intersection numbers of certain tautological classes in the combinatorial Chow ring $A^\bullet(M)$ arising from Grassmannians.
A. Berget, Hunter Spink, Dennis Tseng
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The inverse Kazhdan-Lusztig polynomial of a matroid [PDF]
J. Comb. Theory B, 2020 In analogy with the classical Kazhdan-Lusztig polynomials for Coxeter groups, Elias, Proudfoot and Wakefield introduced the concept of Kazhdan-Lusztig polynomials for matroids.
Alice L. L. Gao, M. H. Xie
semanticscholar +1 more source
Log-concave polynomials II: high-dimensional walks and an FPRAS for counting bases of a matroid [PDF]
Symposium on the Theory of Computing, 2018 We design an FPRAS to count the number of bases of any matroid given by an independent set oracle, and to estimate the partition function of the random cluster model of any matroid in the regime where ...
Nima Anari +3 more
semanticscholar +1 more source
Abstract 3-Rigidity and Bivariate $C_2^1$-Splines II: Combinatorial Characterization
Discrete Analysis, 2022 3-Rigidity and Bivariate $C_2^1$-Splines II: Combinatorial Characterization, Discrete Analysis 2022:3, 32 pp. As its title suggests, this paper follows on from the previous paper published in this journal.
Katie Clinch +2 more
doaj +1 more source
Weighted Tree-Numbers of Matroid Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We give a new formula for the weighted high-dimensional tree-numbers of matroid complexes. This formula is derived from our result that the spectra of the weighted combinatorial Laplacians of matroid complexes consist of polynomials in the weights.
Woong Kook, Kang-Ju Lee
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