Abstract
We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. André on the number of up-down permutations. The analysis uses a transfer operator approach extending the method of Elkies, combined with an identity expressing the volume of a certain polytope in terms of a Schur function.
| Original language | English |
|---|---|
| Pages (from-to) | 157-186 |
| Number of pages | 30 |
| Journal | Israel Journal of Mathematics |
| Volume | 178 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Dec 1 2010 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
Cite this
Enumeration formulas for young tableaux in a diagonal strip. / Baryshnikov, Yuliy; Romik, Dan.
In: Israel Journal of Mathematics, Vol. 178, No. 1, 01.12.2010, p. 157-186.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Enumeration formulas for young tableaux in a diagonal strip
AU - Baryshnikov, Yuliy
AU - Romik, Dan
PY - 2010/12/1
Y1 - 2010/12/1
N2 - We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. André on the number of up-down permutations. The analysis uses a transfer operator approach extending the method of Elkies, combined with an identity expressing the volume of a certain polytope in terms of a Schur function.
AB - We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. André on the number of up-down permutations. The analysis uses a transfer operator approach extending the method of Elkies, combined with an identity expressing the volume of a certain polytope in terms of a Schur function.
UR - http://www.scopus.com/inward/record.url?scp=79251546446&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79251546446&partnerID=8YFLogxK
U2 - 10.1007/s11856-010-0061-6
DO - 10.1007/s11856-010-0061-6
M3 - Article
AN - SCOPUS:79251546446
VL - 178
SP - 157
EP - 186
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
SN - 0021-2172
IS - 1
ER -