Partition inequalities

Partition inequalities for capacitated survivable network design based on directed p-cycles

Discrete Optimization ◽

10.1016/j.disopt.2007.08.002 ◽

2008 ◽

Vol 5 (2) ◽

pp. 415-433 ◽

Cited By ~ 7

Author(s):

Alper Atamtürk ◽

Deepak Rajan

Keyword(s):

Network Design ◽

Survivable Network Design ◽

Survivable Network ◽

Partition Inequalities

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Asymptotically trivial linear homogeneous partition inequalities

Journal of Number Theory ◽

10.1016/j.jnt.2017.08.012 ◽

2018 ◽

Vol 184 ◽

pp. 107-121 ◽

Cited By ~ 1

Author(s):

Jacob Katriel

Keyword(s):

Partition Inequalities

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Separation of partition inequalities for the (1,2)-survivable network design problem

Operations Research Letters ◽

10.1016/s0167-6377(02)00182-7 ◽

2002 ◽

Vol 30 (4) ◽

pp. 265-268 ◽

Cited By ~ 12

Author(s):

Hervé Kerivin ◽

Ali Ridha Mahjoub

Keyword(s):

Network Design ◽

Design Problem ◽

Network Design Problem ◽

Survivable Network Design ◽

Survivable Network ◽

Partition Inequalities

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Node partition inequalities

Design of Survivable Networks - Lecture Notes in Mathematics ◽

10.1007/bfb0088971 ◽

1992 ◽

pp. 91-99

Author(s):

Mechthild Stoer

Keyword(s):

Partition Inequalities

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Separation of partition inequalities with terminals

Discrete Optimization ◽

10.1016/j.disopt.2004.05.001 ◽

2004 ◽

Vol 1 (2) ◽

pp. 129-140 ◽

Cited By ~ 6

Author(s):

Francisco Barahona ◽

Hervé Kerivin

Keyword(s):

Partition Inequalities

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Some Elementary Partition Inequalities and Their Implications

Annals of Combinatorics ◽

10.1007/s00026-019-00433-y ◽

2019 ◽

Vol 23 (2) ◽

pp. 263-284

Author(s):

Alexander Berkovich ◽

Ali Kemal Uncu

Keyword(s):

Partition Inequalities

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Fractional partitions and conjectures of Chern–Fu–Tang and Heim–Neuhauser

Transactions of the American Mathematical Society Series B ◽

10.1090/btran/77 ◽

2021 ◽

Vol 8 (21) ◽

pp. 615-634

Author(s):

Kathrin Bringmann ◽

Ben Kane ◽

Larry Rolen ◽

Zack Tripp

Keyword(s):

Partition Function ◽

Future Study ◽

Partition Functions ◽

Colored Partitions ◽

The Future ◽

Error Terms ◽

Partition Inequalities ◽

User Friendly

Many papers have studied inequalities for partition functions. Recently, a number of papers have considered mixtures between additive and multiplicative behavior in such inequalities. In particular, Chern–Fu–Tang and Heim–Neuhauser gave conjectures on inequalities for coefficients of powers of the generating partition function. These conjectures were posed in the context of colored partitions and the Nekrasov–Okounkov formula. Here, we study the precise size of differences of products of two such coefficients. This allows us to prove the Chern–Fu–Tang conjecture and to show the Heim–Neuhauser conjecture in a certain range. The explicit error terms provided will also be useful in the future study of partition inequalities. These are laid out in a user-friendly way for the researcher in combinatorics interested in such analytic questions.

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