Carla D. Savage

Euler's partition theorem and the combinatorics of l-sequences.

Abstract:

Euler's partition theorem says that the number of ways to partition an integer into odd parts is the same as the number of ways to partition it into distinct parts.

We show how the combinatorics of ``l-sequences'' gives rise not only to a generalization of Euler's theorem (discovered by Bousquet-Mélou and Eriksson in 1997), but also to a generalization of Sylvester's bijective proof. This is joint work with Ae Ja Yee.

The ``l-sequences'' also give rise to a generalization of the binomial coefficient.  In joint work with Nicholas Loehr, we investigate implications and interpretations.

References:

1. MR1607531 (99c:05015)  Bousquet-Mélou, Mireille;  Eriksson, Kimmo. Lecture hall partitions.  Ramanujan J.  1  (1997),  no. 1, 101--111.

2. MR1606188 (99c:05016)  Bousquet-Mélou, Mireille;  Eriksson, Kimmo. Lecture hall partitions. II.  Ramanujan J.  1  (1997),  no. 2, 165--185.

3. C. D. Savage and A. J. Yee,  Euler's partition theorem and the combinatorics of l-sequences,  J. Combin. Theory Ser. A, (article in press).
draft: http://www4.ncsu.edu/~savage/PAPERS/ell_euler96.pdf