M₂-rank differences for overpartitions

Jeremy Lovejoy; Robert Osburn

Displaying similar documents to “M₂-rank differences for overpartitions”

A new rank formula for idempotent matrices with applications

Yong Ge Tian, George P. H. Styan (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that $rank (P^{*} A Q) = rank (P^{*} A) + rank (A Q) - rank (A),$ where $A$ is idempotent, $[P, Q]$ has full row rank and $P^{*} Q = 0$ . Some applications of the rank formula to generalized inverses of matrices are also presented.

Rank conditions for estimability of covariances

G. S. Rogers (1983)

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Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.

Two conjectures regarding the stability of ω-categorical theories

A. Lachlan (1974)

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Co-rank and Betti number of a group

Irina Gelbukh (2015)

Czechoslovak Mathematical Journal

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For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number...

Singular properties of Morley rank

A. Lachlan (1980)

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Spaces of rank-2 matrices over GF(2).

Beasley, LeRoy B. (1999)

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Linearized Rank Estimates and Signed-Rank Estimates for the General Linear Hypothesis

Charles H. Kraft, Constance Van Eeden (1969-1970)

Publications mathématiques et informatique de Rennes

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Zero-term rank preservers of integer matrices

Seok-Zun Song, Young-Bae Jun (2006)

Discussiones Mathematicae - General Algebra and Applications

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The zero-term rank of a matrix is the minimum number of lines (row or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve the zero-term rank of the m × n integer matrices. That is, a linear operator T preserves the zero-term rank if and only if it has the form T(A)=P(A ∘ B)Q, where P, Q are permutation matrices and A ∘ B is the Schur product with B whose entries are all nonzero integers.