8,002 research outputs found
Distinct parts partitions without sequences
Partitions without sequences of consecutive integers as parts have been
studied recently by many authors, including Andrews, Holroyd, Liggett, and
Romik, among others. Their results include a description of combinatorial
properties, hypergeometric representations for the generating functions, and
asymptotic formulas for the enumeration functions. We complete a similar
investigation of partitions into distinct parts without sequences, which are of
particular interest due to their relationship with the Rogers-Ramanujan
identities. Our main results include a double series representation for the
generating function, an asymptotic formula for the enumeration function, and
several combinatorial inequalities.Comment: 15 page
Enumeration of concave integer partitions
An integer partition \lambda of n corresponds, via its Ferrers diagram, to an
artinian monomial ideal I of colength n in the polynomial ring on two
variables. If the partition \lambda corresponds to an integrally closed ideal
we call \lambda concave. We study generating functions for the number of
concave partitions, unrestricted or with at most r parts.Comment: 8 pages. ver 2: Added reference to asymptotic estimate by Gert
Almkvist. ver 3: Minor editing. ver 4: Added reference to Canfield et al,
rewrote section 3 ver 5: Added reference to Andrew
(-1)-enumeration of plane partitions with complementation symmetry
We compute the weighted enumeration of plane partitions contained in a given
box with complementation symmetry where adding one half of an orbit of cubes
and removing the other half of the orbit changes the weight by -1 as proposed
by Kuperberg. We use nonintersecting lattice path families to accomplish this
for transpose-complementary, cyclically symmetric transpose-complementary and
totally symmetric self-complementary plane partitions. For symmetric
transpose-complementary and self-complementary plane partitions we get partial
results. We also describe Kuperberg's proof for the case of cyclically
symmetric self-complementary plane partitions.Comment: 41 pages, AmS-LaTeX, uses TeXDraw; reference adde
- …