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Results tagged with reference-request
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user 23980
This tag is used if a reference is needed in a paper or textbook on a specific result.
0
votes
2
answers
94
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Isometric path cover number of the 2 dimensional grid graph
I am looking for a proof of the fact that at least $2n/3$ isometric paths (i.e. shortest paths between the end points) are required to cover the vertices of the $n\times n$ grid graph (i.e. Cartesian …
- 23.7k
2
votes
Proofs by Schubert calculus and combinatorics
Unimodality of partitions inside a box of size $m\times n$ (i.e. partitions with number of parts at most $m$ and size of the largest part at most $n$) follows from applying Hard Lefschetz Theorem to t …
- 1,305
3
votes
0
answers
268
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A generalization of Rogers-Ramanujan identity
The generalized Rogers-Ramanujan identity has the following form
$$\sum_{k_1\geq\cdots\geq k_r\geq 0}\frac{x^{k_1^2+\cdots +k_r^2+k_i+\cdots +k_r}}{(x)_{k_1-k_2}\cdots (x)_{k_{r-1}-k_r}(x)_{k_r}}=\pr …
- 13.4k
2
votes
0
answers
88
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Rank-unimodality and Sperner property of higher dimensional partitions
I did a google-search but have not been able to find much reference on this problem. So I am asking it here hoping to get some information.
Consider the set of all 4-dimensional Ferrer's diagram cont …
- 1,305
10
votes
2
answers
5k
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Cohen-Lenstra Heuristics reference
I am looking for good references (preferably, books) on Cohen-Lenstra Heuristics (on Real Quadratic fields) which explain in detail the reasons behind its fundamental assumption (higher the cardinalit …
- 5,670