Unmixed bipartite graphs and sublattices of the Boolean lattices

The correspondence between unmixed bipartite graphs and sublattices of the oolean lattice is discussed. By using this correspondence, we show the existence of squarefree quadratic initial ideals of toric ideals arising from minimal vertex covers of unmixed bipartite graphs.Comment: 5 page

A New Galactic Extinction Map of the Cygnus Region

We have made a Galactic extinction map of the Cygnus region with 5' spatial resolution. The selected area is 80^\circ to 90^\circ in the Galactic longitude and -4^\circ to 8^\circ in the Galactic latitude. The intensity at 140 \mum is derived from the intensities at 60 and 100 \mum of the IRAS data using the tight correlation between 60, 100, and 140 \mum found in the Galactic plane. The dust temperature and optical depth are calculated with 5' resolution from the 140 and 100 \mum intensity, and Av is calculated from the optical depth. In the selected area, the mean dust temperature is 17 K, the minimum is 16 K, and the maximum is 30 K. The mean Av is 6.5 mag, the minimum is 0.5 mag, and the maximum is 11 mag. The dust temperature distribution shows significant spatial variation on smaller scales down to 5'. Because the present study can trace the 5'-scale spatial variation of the extinction, it has an advantage over the previous studies, such as the one by Schlegel, Finkbeiner, & Davis, who used the COBE/DIRBE data to derive the dust temperature distribution with a spatial resolution of 1^\circ. The difference of Av between our map and Schlegel et al.'s is \pm 3 mag. A new extinction map of the entire sky can be produced by applying the present method.Comment: 27 pages, 14 figures, accepted for publication in Ap

Betti number sequences of simplicial complexes, Cohen-Macaulay types and Mbius functions of partially ordered sets, and related topics

We give a survey of some recent results on bt·(k[6]) = dimk Torf(k[6], k) of the face ring (Stanley-Reisner ring) k[6] of a simplicial complex 6. In particular, we study Cohen-Macaulay types and canonical modules of partially ordered sets

Buchsbaum complexes with linear resolutions

We study the Betti numbers which appear in a minimal free res­olution of the Stanley-Reisner ring k[.6.] of a Buchsbaum complex .6. and find a characterization of Buchsbaum complexes .6. for which a minimal free resolution of k[.6.] is linear

Hochster's formula on Betti numbers and Buchsbaum complexes

The Betti numbers dimk.ToriA(k[ ],k) with i > v - d of the Stanley-Reisner ring k[ ] = A/I of a Buchsbaum complex of dimension d - 1 ouer a field k with v uertices are studied