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Noncommutative Enumeration in Graded Posets
| Content Provider | Semantic Scholar |
|---|---|
| Author | Billera, Louis J. Liu, Niandong |
| Copyright Year | 2000 |
| Abstract | We define a noncommutative algebra of flag-enumeration functionals on graded posets and show it to be isomorphic to the free associative algebra on countably many generators. Restricted to Eulerian posets, this ring has a particularly appealing presentation with kernel generated by Euler relations. A consequence is that even on Eulerian posets, the algebra is free, with generators corresponding to odd jumps in flags. In this context, the coefficients of the cd-index provide a graded basis. |
| Starting Page | 7 |
| Ending Page | 24 |
| Page Count | 18 |
| File Format | PDF HTM / HTML |
| DOI | 10.1023/A:1008703300280 |
| Volume Number | 12 |
| Alternate Webpage(s) | http://www.maths.tcd.ie/EMIS/journals/JACO/Volume12_1/tv641141uk22445q.fulltext.pdf |
| Alternate Webpage(s) | http://www.math.cornell.edu/~billera/papers/euler.ps |
| Alternate Webpage(s) | https://doi.org/10.1023/A%3A1008703300280 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |