Geodesic
Linked partition ideals, directed graphs and \(q\)-multi-summations
Shane Chern1
1The Pennsylvania State University
The electronic journal of combinatorics, Tome 27 (2020) no. 3
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In this paper, we start by considering generating function identities for linked partition ideals in the setting of basic graph theory. Then our attention is turned to $q$-difference systems, which eventually lead to a factorization problem of a special type of column functional vectors involving $q$-multi-summations. Using a recurrence relation satisfied by certain $q$-multi-summations, we are able to provide non-computer-assisted proofs of some Andrews--Gordon type generating function identities. These proofs also have an interesting connection with binary trees. Further, we give illustrations of constructing a linked partition ideal, or more loosely, a set of integer partitions whose generating function corresponds to a given set of special $q$-multi-summations.
DOI : 10.37236/9446
Classification : 11P84, 05A17, 05C05, 05C20, 33D70
Mots-clés : \(q\)-multi-summations, linked partition ideals, \(q\)-differential systems

Shane Chern  1

1 The Pennsylvania State University 
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     author = {Shane Chern},
     title = {Linked partition ideals, directed graphs and \(q\)-multi-summations},
     journal = {The electronic journal of combinatorics},
     year = {2020},
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Shane Chern. Linked partition ideals, directed graphs and \(q\)-multi-summations. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/9446

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