A 2 × 2 factorial study evaluated effects of cow wintering system and last trimester CP supplementation on performance of beef cows and steer progeny over a 3-yr period. Pregnant composite cows (Red Angus × Simmental) grazed winter range (WR; n = 4/yr) or corn residue (CR; n = 4/yr) during winter and within grazing treatment received 0.45 kg/d (DM) 28% CP cubes (PS; n = 4/yr) or no supplement (NS; n = 4/yr). Offspring steer calves entered the feedlot 14 d postweaning and were slaughtered 222 d later. Precalving BW was greater (P = 0.02) for PS than NS cows grazing WR, whereas precalving BCS was greater (P < 0.001) for cows grazing CR compared with WR. Calf birth BW was greater (P = 0.02) for CR than WR and tended to be greater (P = 0.11) for PS than NS cows. Prebreeding BW and BCS were greater (P ≤ 0.001) for CR than WR cows and PS than NS (P = 0.006) cows. At weaning, CR cows were heavier (P < 0.001) than WR cows but had similar BCS (P = 0.74). Cow weaning BW and BCS were not affected (P > 0.32) by PS.Calf weaning BW was less (P = 0.01) for calves from NS cows grazing WR compared with all other treatments. Pregnancy rate was unaffected by treatment (P > 0.39). Steer ADG, 12th-rib fat, yield grade, and LM area (P > 0.10) were similar among all treatments. However, final BW and HCW (P = 0.02) were greater for steers from PS-WR than NS-WR cows. Compared with steers from NS cows, steers from PS cows had greater marbling scores (P = 0.004) and a greater (P = 0.04) proportion graded USDA Choice or greater. Protein supplementation of dams increased the value of calves at weaning (P = 0.03) and of steers at slaughter regardless of winter grazing treatment (P = 0.005). Calf birth and weaning BW were increased by grazing CR during the winter. Calf weaning BW was increased by PS of the dam if the dam grazed WR. Compared with steers from NS cows, steer progeny from PS cows had a greater quality grade with no (P = 0.26) effect on yield grade. These data support a late gestation dam nutrition effect on calf production via fetal programming.

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Abstract. We generalize the definition and enumeration of spanning trees from the setting of graphs to that of arbitrary-dimensional simplicial complexes ∆, extending an idea due to G. Kalai. We prove a simplicial version of the Matrix-Tree Theorem that counts simplicial spanning trees, weighted by the squares of the orders of their top-dimensional integral homology groups, in terms of the Laplacian matrix of ∆. As in the graphic case, one can obtain a more finely weighted generating function for simplicial spanning trees by assigning an indeterminate to each vertex of ∆ and replacing the entries of the Laplacian with Laurent monomials. When ∆ is a shifted complex, we give a combinatorial interpretation of the eigenvalues of its weighted Laplacian and prove that they determine its set of faces uniquely, generalizing known results about threshold graphs and unweighted Laplacian eigenvalues of shifted complexes.

Abstract. A long-standing conjecture of Stanley states that every CohenMacaulay simplicial complex is partitionable. We disprove the conjecture by constructing an explicit counterexample. Due to a result of Herzog, Jahan and Yassemi, our construction also disproves the conjecture that the Stanley depth of a monomial ideal is always at least its depth.

Let T be an unrooted tree. The chromatic symmetric function X T , introduced by Stanley, is a sum of monomial symmetric functions corresponding to proper colorings of T . The subtree polynomial S T , first considered under a different name by Chaudhary and Gordon, is the bivariate generating function for subtrees of T by their numbers of edges and leaves. We prove that S T = Φ, X T , where ·,· is the Hall inner product on symmetric functions and Φ is a certain symmetric function that does not depend on T . Thus the chromatic symmetric function is a stronger isomorphism invariant than the subtree polynomial. As a corollary, the path and degree sequences of a tree can be obtained from its chromatic symmetric function. As another application, we exhibit two infinite families of trees (spiders and some caterpillars), and one family of unicyclic graphs (squids) whose members are determined completely by their chromatic symmetric functions.