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Four factorization formulas for plane partitions
- Publication Year :
- 2015
-
Abstract
- All ten symmetry classes of plane partitions that fit in a given box are known to be enumerated by simple product formulas, but there is still no unified proof for all of them. Progress towards this goal can be made by establishing identities connecting the various symmetry classes. We present in this paper four such identities, involving all ten symmetry classes. We discuss their proofs and generalizations. The main result of this paper is to give a generalization of one of them, in the style of the identity presented in "A factorization theorem for rhombus tilings," M. Ciucu and C. Krattenthaler, arXiv:1403.3323.<br />14 pages
- Subjects :
- Statistical Mechanics (cond-mat.stat-mech)
Generalization
Applied Mathematics
General Mathematics
010102 general mathematics
FOS: Physical sciences
0102 computer and information sciences
Mathematical proof
01 natural sciences
Combinatorics
symbols.namesake
Identity (mathematics)
Factorization
010201 computation theory & mathematics
Simple (abstract algebra)
Product (mathematics)
Weierstrass factorization theorem
FOS: Mathematics
symbols
Mathematics - Combinatorics
Combinatorics (math.CO)
0101 mathematics
Symmetry (geometry)
Condensed Matter - Statistical Mechanics
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....6d10590ee44c15ccdbfcba9f98de6e38