# On partitions with fixed number of even-indexed and odd-indexed odd parts

@article{Berkovich2015OnPW, title={On partitions with fixed number of even-indexed and odd-indexed odd parts}, author={Alexander Berkovich and Ali Kemal Uncu}, journal={arXiv: Number Theory}, year={2015} }

This article is an extensive study of partitions with fixed number of odd and even-indexed odd parts. We use these partitions to generalize recent results of C. Savage and A. Sills. Moreover, we derive explicit formulas for generating functions for partitions with bounds on the largest part, the number of parts and with a fixed value of BG-rank or with a fixed value of alternating sum of parts. We extend the work of C. Boulet, and as a result, obtain a four-variable generalization of Gaussian… CONTINUE READING

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VIEW 2 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 18 REFERENCES

## On a Partition Theorem of Göllnitz and Quartic Transformations

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## On partition functions of Andrews and Stanley

VIEW 1 EXCERPT

## A new companion to Capparelli's identities

VIEW 1 EXCERPT

## Some remarks on sign-balanced and maj-balanced posets

VIEW 1 EXCERPT

## A four-parameter partition identity

VIEW 12 EXCERPTS

HIGHLY INFLUENTIAL

## The Theory of Partitions

VIEW 2 EXCERPTS