The umbral transfer-matrix method. III: Counting animals. par This is the third part of the five-part saga on the umbral transfer-matrix method, based on Gian-Carlo Rota’s seminal notion of the umbra. In this article we describe the Maple package ZOO that for any specific $k$, automatically constructs an umbral scheme for enumerating “$k$-board” lattice animals (polyominoes) on the two-dimensional square lattice. Such umbral schemes enable counting these important classes of animals in polynomial time as opposed to the exponential time that is required for counting all animals.
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References in zbMATH (referenced in 4 articles )
Showing results 1 to 4 of 4.
- Baxter, Andrew; Nakamura, Brian; Zeilberger, Doron: Automatic generation of theorems and proofs on enumerating consecutive-Wilf classes (2013)
- Ekhad, Shalosh B.; Zeilberger, Doron: Using Rota’s Umbral calculus to enumerate Stanley’s $P$-partitions (2008)
- Zeilberger, Doron: The umbral transfer-matrix method. III: Counting animals (2001)
- Zeilberger, Doron: The umbral transfer-matrix method. I: Foundations (2000)