Occupational Redemption

In Occupational Hazards in the February 1981 Word Ways, Richard E. Douglass suggests that various jobholders can be gotten rid of in ways more euphemistically ambiguous than simply being fired, canned, or sacked. For the most part, he plays upon the semantic properties of absorbed roots conjoined with the negative prefixes de- and dis- and shows how a nobleman would be discounted, distributed or subject to delivery and a tennis player disadvantaged or defaulted (or, we add, deserved or deduced). In a more optimistic vein, let us ask ourselves how, using the prefix re- and the suffix -ed, we can describe the reinstatement to their jobs of the following people

Components of Gr\"obner strata in the Hilbert scheme of points

We fix the lexicographic order $\prec$ on the polynomial ring $S=k[x_{1},...,x_{n}]$ over a ring $k$. We define \Hi^{\prec\Delta}_{S/k}, the moduli space of reduced Gr\"obner bases with a given finite standard set $\Delta$, and its open subscheme \Hi^{\prec\Delta,\et}_{S/k}, the moduli space of families of #\Delta points whose attached ideal has the standard set $\Delta$. We determine the number of irreducible and connected components of the latter scheme; we show that it is equidimensional over ${\rm Spec}\,k$; and we determine its relative dimension over ${\rm Spec} k$. We show that analogous statements do not hold for the scheme \Hi^{\prec\Delta}_{S/k}. Our results prove a version of a conjecture by Bernd Sturmfels.Comment: 49 page

The States We\u27re In

Celebrated June 14, Flag Day commemorates the adoption by the Continental Congress of the Stars and Stripes in 1777 as the official flag of America. The thirteen stripes on the flag represent the original colonies and the fifty stars the united states of the United States

What do You Call a Naked Grizzly?

Homophones are words that sound alike but are spelled differently and have different meanings. Examples of sound-alike words are flair and flare, colonel and kernel, and poor, pore and pour. Here is a puzzle designed to test your ear for homophones