Empowered Women Empower Women

Good afternoon and thank you for your determination to hold this important event today regardless of the weather. When Jenny said that we would go forward rain, sleet, or snow, I did not anticipate that we would have all three in the same day! Maybe your determination derives from the residual spirit of a group of women who gathered here 100 years ago, also determined, but that time they were determined to ensure that their community acknowledged their right to vote. They were empowered, excited, and ready to act because, five years prior, in 1915, Katherine Wentworth of the Pennsylvania Women’s Suffrage Association, commissioned the Justice Bell, also known as the Women’s Liberty Bell or the Suffrage Bell. Once it was done, they loaded in the back of a flatbed truck and drove it to all 67 Pennsylvania counties. But they chained the clapper so it would not ring to symbolize the silence imposed upon women through the denial of the right to vote. When the 19th Amendment finally was ratified in 1920, Wentworth and her fellow suffragists gathered in Philadelphia to ring the bell 48 times to honor the 48 states of the Union at the time. All courthouses and churches in Pennsylvania were supposed to join in a statewide ringing at 4 pm that afternoon. The women of Gettysburg were gathered here, anxiously awaiting 4 pm. It came and passed. 4:01. 4:02. Then, as the Gettysburg Times reported “they decided that action would have to be taken by themselves.” They rushed the courthouse and proceeded to ring the bell “several minutes,” which, as the Times also reported, “the women thoroughly enjoyed . . . until officials arrived and relieved them.” Sometimes, you have to take matters into your own hands if you want to make a difference in your community. [excerpt

The Prospects for Family Business in Research Universities

Family business shows the promise of becoming a respected scholarly field in research universities. However, success is not a given. We inquire about its prospects, with reference to the sociology of science. A key requirement for success that has been met is identification with an important and distinctive domain of inquiry. This domain is at the intersection two phenomena - of kinship and business - but more attention has been paid to enterprise than to kinship. We suggest that this creates important windows for theoretical development, an important requirement for a core presence in research universities. We further suggest additional priorities, such as progress in journal and research quality, more developed links to pressing social issues such as international business, inclusion of family business issues in the credit curriculum, and faculty lines that create research continuity and legitimize research on family business

Inhomogeneous lattice paths, generalized Kostka polynomials and An−1_{n-1} supernomials

Inhomogeneous lattice paths are introduced as ordered sequences of rectangular Young tableaux thereby generalizing recent work on the Kostka polynomials by Nakayashiki and Yamada and by Lascoux, Leclerc and Thibon. Motivated by these works and by Kashiwara's theory of crystal bases we define a statistic on paths yielding two novel classes of polynomials. One of these provides a generalization of the Kostka polynomials while the other, which we name the A$_{n-1}$ supernomial, is a $q$-deformation of the expansion coefficients of products of Schur polynomials. Many well-known results for Kostka polynomials are extended leading to representations of our polynomials in terms of a charge statistic on Littlewood-Richardson tableaux and in terms of fermionic configuration sums. Several identities for the generalized Kostka polynomials and the A$_{n-1}$ supernomials are proven or conjectured. Finally, a connection between the supernomials and Bailey's lemma is made.Comment: 44 pages, figures, AMS-latex; improved version to appear in Commun. Math. Phys., references added, some statements clarified, relation to other work specifie

Supernomial coefficients, polynomial identities and qq-series

$q$-Analogues of the coefficients of $x^a$ in the expansion of $\prod_{j=1}^N (1+x+...+x^j)^{L_j}$ are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of the ``$q$-supernomial coefficients'' are derived, and a combinatorial interpretation using generalized Durfee dissection partitions is given. Polynomial identities of boson-fermion-type, based on the continued fraction expansion of $p/k$ and involving the $q$-supernomial coefficients, are proven. These include polynomial analogues of the Andrews-Gordon identities. Our identities unify and extend many of the known boson-fermion identities for one-dimensional configuration sums of solvable lattice models, by introducing multiple finitization parameters.Comment: 34 pages, Latex2e, figures; improved versio