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We consider two families of plane partitions: totally symmetric self-complementary plane partitions (TSSCPPs) and cyclically symmetric transpose complement plane partitions (CSTCPPs). If T (n) and C(n) are the numbers of such plane partitions in a 2n× 2n× 2n box, then ord2(T (n)) = ord2(C(n)) for all n ≥ 1. We also discuss various consequences, along with… (More)

In this paper, we consider sequences comprised of n (m− 1)’s and r −1’s (where m ≥ 2) with the sum of each subsequence of the first j terms nonnegative. We will denote the number of such sequences as { n r } m−1. Our goal is to present various results involving { n r } m−1, including an interpretation of the sequences counted by { n r } m−1 which truly… (More)

- Darrin D. Frey, James A. Sellers
- Ars Comb.
- 2004

We let A(n) equal the number of n×n alternating sign matrices. From the work of a variety of sources, we know that

- D D Frey
- Biotechnology and bioengineering
- 1990

- Darrin D. Frey, James A. Sellers
- Ars Comb.
- 2005

In this note, we consider arithmetic properties of the function K(n) = (2n)!(2n + 2)! (n− 1)!(n + 1)!2(n + 2)! which counts the number of two–legged knot diagrams with one self– intersection and n − 1 tangencies. This function recently arose in a paper by Jacobsen and Zinn–Justin on the enumeration of knots via a transfer matrix approach. Using elementary… (More)

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