Some of the research work conducted by Dennis Stanton in the field of algebraic combinatorics and special functions are discussed. His early works include orthogonal polynomials of basic hypergeometric type and relations between several orthogonal polynomials of basic hypergeometric type and finite groups of Lie type. Stanton together with Viennot developed a combinatorial theory for the q-Hermite polynomials and the Askey Wilson integral. Stanton also worked on the Rogers Ramanujan identities giving infinite family of Rogers Ramanujan identities. His combinatorial work includes t-cores and t-quotients of partitions, and the abacus bijection from modular representation theory of the symmetric group. Another persistent theme in Dennis combinatorial work is unimodality and its relation to partially ordered sets.
Bibliographical noteFunding Information:
Dennis’s generosity extended to other aspects of his work with PhD students. He not only supported us with his time and energy, but he would find support for us as we traveled to conferences, looked for jobs and began developing our own careers. He once casually announced he had gotten an NSF grant to support me so that I could focus on research during one of my last semesters — an endeavor I now realize takes enormous effort. He never made a big deal out of his generosity. Whenever I would thank him for picking up a check for dinner, writing letters of recommendation and spending hours sharing his deep knowledge of mathematics he would simply shrug and smile.