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9 papers · 2 filters
A note on two identities arising from enumeration of convex polyominoes
Victor J. W. Guo, Jiang Zeng
Motivated by some binomial coefficients identities encountered in our approach to the enumeration of convex polyominoes, we prove some more general identities of the same type, one…
Applicability of the -Analogue of Zeilberger's Algorithm
William Y. C. Chen, Qing-Hu Hou, Yan-Ping Mu
The applicability or terminating condition for the ordinary case of Zeilberger's algorithm was recently obtained by Abramov. For the -analogue, the question of whether a bivaria…
Old and young leaves on plane trees
William Y. C. Chen, Emeric Deutsch, Sergi Elizalde
A leaf of a plane tree is called an old leaf if it is the leftmost child of its parent, and it is called a young leaf otherwise. In this paper we enumerate plane trees with a given…
Transformations of Border Strips and Schur Function Determinants
William Y. C. Chen, Guo-Guang Yan, Arthur L. B. Yang
We introduce the notion of the cutting strip of an outside decomposition of a skew shape, and show that cutting strips are in one-to-one correspondence with outside decompositions…
Reduction of -Regular Noncrossing Partitions
William Y. C. Chen, Eva Y. P. Deng, Rosena R. X. Du
In this paper, we present a reduction algorithm which transforms -regular partitions of to -regular partitions of . We show that this algori…
Partition Analysis and Symmetrizing Operators
Amy M. Fu, Alain Lascoux
Using a symmetrizing operator, we give a new expression for the Omega operator used by MacMahon in Partition Analysis, and given a new life by Andrews and his coworkers. Our result…