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Mark Giroux

Publications and source records attributed to Mark Giroux.

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A Lower Bound for Kruskal's Weak Tree Function tree(3)

We establish an explicit lower bound for Kruskal's weak tree function at n=3, proving that tree(3) >= 844,424,930,131,960 = 3 * 2^48 - 8. This is achieved by constructing an explicit sequence of unlabeled rooted trees satisfying the constraints of the weak tree function and carefully analyzing the combinatorics of the "leg elimination" process. Our bound significantly exceeds previous estimates and demonstrates that even for small arguments, the weak tree function exhibits rapid growth.

math.CO

The Multiphase Intergalactic Medium towards PKS 2155-304

We study the cluster of H I and O VI absorption systems and the claimed detection of O VIII absorption from the intergalactic medium at z ~ 0.0567, associated with a group of galaxies toward the BL Lac object PKS 2155-304. As measured by spectrographs on the Hubble Space Telescope, Far Ultraviolet Spectroscopic Explorer, and Chandra, this system appears to contain gas at a variety of temperatures. We analyze this multi-phase gas in a clumpy-infall model. From the absence of C IV and Si III absorption in the Ly-alpha clouds, we infer metallicities less than 2.5-10% of solar values. The only metals are detected in two O VI absorption components, offset by +/- 400 km/s from the group barycenter (cz ~ 16,600 km/s). The O VI components may signify "nearside" and "backside" infall into the group potential well, which coincides with the claimed O VIII absorption. If the claimed O VIII detection is real, our analysis suggests that clusters of strong Ly-alpha and O VI absorbers, associated with groups of galaxies, may be the "signposts" of shock-heated, metal-enriched baryons. Through combined UV and X-ray spectra of H I and O VI, O VII, and O VIII, one may be able to clarify the heating mechanism of this multiphase gas.

astro-ph