4,816 research outputs found
Congruence conditions, parcels, and Tutte polynomials of graphs and matroids
Let be a matrix and be the matroid defined by linear dependence on
the set of column vectors of Roughly speaking, a parcel is a subset of
pairs of functions defined on to an Abelian group satisfying a
coboundary condition (that is a flow over relative to ) and a
congruence condition (that the size of the supports of and satisfy some
congruence condition modulo an integer). We prove several theorems of the form:
a linear combination of sizes of parcels, with coefficients roots of unity,
equals an evaluation of the Tutte polynomial of at a point
on the complex hyperbola $(\lambda - 1)(x-1) = |A|.
Maximum size binary matroids with no AG(3,2)-minor are graphic
We prove that the maximum size of a simple binary matroid of rank
with no AG(3,2)-minor is and characterise those matroids
achieving this bound. When , the graphic matroid is the
unique matroid meeting the bound, but there are a handful of smaller examples.
In addition, we determine the size function for non-regular simple binary
matroids with no AG(3,2)-minor and characterise the matroids of maximum size
for each rank
Murine terminal deoxynucleotidyl transferase: cellular distribution and response to cortisone
The mouse thymus contains two forms of terminal deoxynucleotidyl transferase (TdT) which are distinguishable by the salt concentration necessary to elute them from a phosphocellulose column, by their distrubtion among the thymocyte subpopulations, and by their sensitivity to cortisone treatment. In the whole thymus the later eluting peak (peak II) is the predominant one with about 3-10% of the total activity appearing in peak I. Both peak I and peak II activities are most sensitively assayed by the polymerization of dGMP onto an oligo(dA) primer. The minor population of thymocytes which is less dense and cortisone-resistant contains a higher specific activity of peak I TdT. The majority of TdT activity is, however, found in the major population of thymocytes which occurs in the center region of a bovine serum albumin gradient and is cortisone-sensitive. A very low level of an activity indistinguishable from peak II TdT activity is also detected in the mouse bone marrow. Other tissues, such as spleen, liver, heart, and brain lack detectable amounts of TdT activity
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