The Experts below are selected from a list of 114 Experts worldwide ranked by ideXlab platform
Jan Vondrák - One of the best experts on this subject based on the ideXlab platform.
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Wide partitions, Latin tableaux, and Rota's basis conjecture
Advances in Applied Mathematics, 2003Co-Authors: Timothy Y. Chow, C. Kenneth Fan, Michel X. Goemans, Jan VondrákAbstract:AbstractSay that μ is a “subpartition” of an integer partition λ if the multiset of parts of μ is a submultiset of the parts of λ, and define an integer partition λ to be “wide” if for every subpartition μ of λ, μ⩾μ′ in dominance order (where μ′ denotes the conjugate of μ). Then Brian Taylor and the first author have conjectured that an integer partition λ is wide if and only if there exists a tableau of shape λ such that (1) for all i, the entries in the ith row of the tableau are precisely the integers from 1 to λi inclusive, and (2) for all j, the entries in the Jth Column of the tableau are pairwise distinct. This conjecture was originally motivated by Rota's basis conjecture and, if true, yields a new class of integer multiflow problems that satisfy max-flow min-cut and integrality. Wide partitions also yield a class of graphs that satisfy “delta-conjugacy” (in the sense of Greene and Kleitman), and the above conjecture implies that these graphs furthermore have a completely saturated stable set partition. We present several partial results, but the conjecture remains very much open
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Wide Partitions, Latin Tableaux, and Rota's Basis Conjecture
2002Co-Authors: Timothy Y. Chow, Michel X. Goemans, Kenneth C. Fan, Jan VondrákAbstract:Say that µ is a "subpartition" of an integer partition if the multiset of parts of is a submultiset of the parts of , and de ne an integer partition to be \wide" if for every subpartition of , in dominance order (where denotes the conjugate of ). Then Brian Taylor and the rst author have conjectured that an integer partition is wide if and only if there exists a tableau of shape such that (1) for all i, the entries in the ith row of the tableau are precisely the integers from 1 to i inclusive, and (2) for all j, the entries in the Jth Column of the tableau are pairwise distinct. This conjecture was originally motivated by Rota's basis conjecture and, if true, yields a new class of integer multiow problems that satisfy max-ow min-cut and integrality. Wide partitions also yield a class of graphs that satisfy \delta-conjugacy" (in the sense of Greene and Kleitman), and the above conjecture implies that these graphs furthermore have a completely saturated stable set partition. We present several partial results, but the conjecture remains very much open
Timothy Y. Chow - One of the best experts on this subject based on the ideXlab platform.
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Wide partitions, Latin tableaux, and Rota's basis conjecture
Advances in Applied Mathematics, 2003Co-Authors: Timothy Y. Chow, C. Kenneth Fan, Michel X. Goemans, Jan VondrákAbstract:AbstractSay that μ is a “subpartition” of an integer partition λ if the multiset of parts of μ is a submultiset of the parts of λ, and define an integer partition λ to be “wide” if for every subpartition μ of λ, μ⩾μ′ in dominance order (where μ′ denotes the conjugate of μ). Then Brian Taylor and the first author have conjectured that an integer partition λ is wide if and only if there exists a tableau of shape λ such that (1) for all i, the entries in the ith row of the tableau are precisely the integers from 1 to λi inclusive, and (2) for all j, the entries in the Jth Column of the tableau are pairwise distinct. This conjecture was originally motivated by Rota's basis conjecture and, if true, yields a new class of integer multiflow problems that satisfy max-flow min-cut and integrality. Wide partitions also yield a class of graphs that satisfy “delta-conjugacy” (in the sense of Greene and Kleitman), and the above conjecture implies that these graphs furthermore have a completely saturated stable set partition. We present several partial results, but the conjecture remains very much open
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Wide Partitions, Latin Tableaux, and Rota's Basis Conjecture
2002Co-Authors: Timothy Y. Chow, Michel X. Goemans, Kenneth C. Fan, Jan VondrákAbstract:Say that µ is a "subpartition" of an integer partition if the multiset of parts of is a submultiset of the parts of , and de ne an integer partition to be \wide" if for every subpartition of , in dominance order (where denotes the conjugate of ). Then Brian Taylor and the rst author have conjectured that an integer partition is wide if and only if there exists a tableau of shape such that (1) for all i, the entries in the ith row of the tableau are precisely the integers from 1 to i inclusive, and (2) for all j, the entries in the Jth Column of the tableau are pairwise distinct. This conjecture was originally motivated by Rota's basis conjecture and, if true, yields a new class of integer multiow problems that satisfy max-ow min-cut and integrality. Wide partitions also yield a class of graphs that satisfy \delta-conjugacy" (in the sense of Greene and Kleitman), and the above conjecture implies that these graphs furthermore have a completely saturated stable set partition. We present several partial results, but the conjecture remains very much open
Michel X. Goemans - One of the best experts on this subject based on the ideXlab platform.
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Wide partitions, Latin tableaux, and Rota's basis conjecture
Advances in Applied Mathematics, 2003Co-Authors: Timothy Y. Chow, C. Kenneth Fan, Michel X. Goemans, Jan VondrákAbstract:AbstractSay that μ is a “subpartition” of an integer partition λ if the multiset of parts of μ is a submultiset of the parts of λ, and define an integer partition λ to be “wide” if for every subpartition μ of λ, μ⩾μ′ in dominance order (where μ′ denotes the conjugate of μ). Then Brian Taylor and the first author have conjectured that an integer partition λ is wide if and only if there exists a tableau of shape λ such that (1) for all i, the entries in the ith row of the tableau are precisely the integers from 1 to λi inclusive, and (2) for all j, the entries in the Jth Column of the tableau are pairwise distinct. This conjecture was originally motivated by Rota's basis conjecture and, if true, yields a new class of integer multiflow problems that satisfy max-flow min-cut and integrality. Wide partitions also yield a class of graphs that satisfy “delta-conjugacy” (in the sense of Greene and Kleitman), and the above conjecture implies that these graphs furthermore have a completely saturated stable set partition. We present several partial results, but the conjecture remains very much open
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Wide Partitions, Latin Tableaux, and Rota's Basis Conjecture
2002Co-Authors: Timothy Y. Chow, Michel X. Goemans, Kenneth C. Fan, Jan VondrákAbstract:Say that µ is a "subpartition" of an integer partition if the multiset of parts of is a submultiset of the parts of , and de ne an integer partition to be \wide" if for every subpartition of , in dominance order (where denotes the conjugate of ). Then Brian Taylor and the rst author have conjectured that an integer partition is wide if and only if there exists a tableau of shape such that (1) for all i, the entries in the ith row of the tableau are precisely the integers from 1 to i inclusive, and (2) for all j, the entries in the Jth Column of the tableau are pairwise distinct. This conjecture was originally motivated by Rota's basis conjecture and, if true, yields a new class of integer multiow problems that satisfy max-ow min-cut and integrality. Wide partitions also yield a class of graphs that satisfy \delta-conjugacy" (in the sense of Greene and Kleitman), and the above conjecture implies that these graphs furthermore have a completely saturated stable set partition. We present several partial results, but the conjecture remains very much open
C. Kenneth Fan - One of the best experts on this subject based on the ideXlab platform.
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Wide partitions, Latin tableaux, and Rota's basis conjecture
Advances in Applied Mathematics, 2003Co-Authors: Timothy Y. Chow, C. Kenneth Fan, Michel X. Goemans, Jan VondrákAbstract:AbstractSay that μ is a “subpartition” of an integer partition λ if the multiset of parts of μ is a submultiset of the parts of λ, and define an integer partition λ to be “wide” if for every subpartition μ of λ, μ⩾μ′ in dominance order (where μ′ denotes the conjugate of μ). Then Brian Taylor and the first author have conjectured that an integer partition λ is wide if and only if there exists a tableau of shape λ such that (1) for all i, the entries in the ith row of the tableau are precisely the integers from 1 to λi inclusive, and (2) for all j, the entries in the Jth Column of the tableau are pairwise distinct. This conjecture was originally motivated by Rota's basis conjecture and, if true, yields a new class of integer multiflow problems that satisfy max-flow min-cut and integrality. Wide partitions also yield a class of graphs that satisfy “delta-conjugacy” (in the sense of Greene and Kleitman), and the above conjecture implies that these graphs furthermore have a completely saturated stable set partition. We present several partial results, but the conjecture remains very much open
Tiefeng Jiang - One of the best experts on this subject based on the ideXlab platform.
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The asymptotic distributions of the largest entries of sample correlation matrices
The Annals of Applied Probability, 2004Co-Authors: Tiefeng JiangAbstract:Let X_n=(x_{ij}) be an n by p data matrix, where the n rows form a random sample of size n from a certain p-dimensional population distribution. Let R_n=(\rho_{ij}) be the p\times p sample correlation matrix of X_n; that is, the entry \rho_{ij} is the usual Pearson's correlation coefficient between the ith Column of X_n and Jth Column of X_n. For contemporary data both n and p are large. When the population is a multivariate normal we study the test that H_0: the p variates of the population are uncorrelated. A test statistic is chosen as L_n=max_{i\ne j}|\rho_{ij}|. The asymptotic distribution of L_n is derived by using the Chen-Stein Poisson approximation method. Similar results for the non-Gaussian case are also derived.
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The asymptotic distributions of the largest entries of sample correlation matrices
2004Co-Authors: Tiefeng JiangAbstract:Let Xn = (xij) be an n by p data matrix, where the n rows form a random sample of size n from a certain p-dimensional population distribution. Let Rn = (ρij) be the p×p sample correlation matrix of Xn; that is, the entry ρij is the usual Pearson’s correlation coefficient between the ith Column of Xn and Jth Column of Xn. For contemporary data both n and p are large. When the population is a multivariate normal we study the test that H0: the p variates of the population are uncorrelated. A test statistic is chosen as Ln = maxi̸=j |ρij|. The asymptotic distribution of Ln is derived by using the Chen–Stein Poisson approximation method. Similar results for the non-Gaussian case are also derived. 1. Introduction. Let Xn = (xij) be an n by p data matrix, where the n rows are observations from a certain multivariate distribution and each of p Columns is an n observation from a variable of the population distribution. Let ρij be the Pearson correlation coefficient between the ith and jt
