5 Citations
Cayley compositions, partitions, polytopes, and geometric bijections
- MathematicsJ. Comb. Theory, Ser. A
- 2014
Effective poset inequalities
- MathematicsArXiv
- 2022
. We explore inequalities on linear extensions of posets and make them effective in different ways. First, we study the Bj¨orner–Wachs inequality and generalize it to inequalities on order polynomials…
Other Generalizations of Continued Fractions
- Mathematics
- 2013
In this chapter we present some other generalizations of regular continued fractions to the multidimensional case. The main goal for us here is to give different geometric constructions related to…
Limit Shapes via Bijections
- MathematicsCombinatorics, Probability and Computing
- 2018
We compute the limit shape for several classes of restricted integer partitions, where the restrictions are placed on the part sizes rather than the multiplicities. Our approach utilizes certain…
Complexity problems in enumerative combinatorics
- MathematicsProceedings of the International Congress of Mathematicians (ICM 2018)
- 2019
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
References
SHOWING 1-10 OF 24 REFERENCES
Partition identities and geometric bijections
- Mathematics
- 2004
We present a geometric framework for a class of partition identities. We show that there exists a unique bijection proving these identities, which satisfies certain linearity conditions. In…
The two-way rewriting in action: Removing the mystery of Euler-Glaisher's map
- MathematicsDiscret. Math.
- 2007
Bijections and Congruences for Generalizations of Partition Identities of Euler and Guy
- MathematicsElectron. J. Comb.
- 2004
Extensions of Richard Guy's result are considered, which naturally lead to a new algorithm for producing bijections between various equivalent partition ideals of order 1, as well as to two new infinite families of parity results which follow from Euler's Pentagonal Number Theorem and a well-known series-product identity of Jacobi.
Method for constructing bijections for classical partition identities.
- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1981
It appears that the construction of a bijection between the partitions of n with parts congruent to 1 or 4 (mod 5) and the partitions with parts differing by at least 2 and an algorithm for constructing bijections for other identities of Rogers-Ramanujan type such as the Gordon identities is found.
Finding direct partition bijections by two-directional rewriting techniques
- MathematicsDiscret. Math.
- 2004
Bijective Proofs of Some Classical Partition Identities
- MathematicsJ. Comb. Theory, Ser. A
- 1982
Partition bijections, a survey
- Mathematics
- 2006
We present an extensive survey of bijective proofs of classical partitions identities. While most bijections are known, they are often presented in a different, sometimes unrecognizable way. Various…