# Restricted partitions and q-Pell numbers

Open Mathematics (2011)

- Volume: 9, Issue: 2, page 346-355
- ISSN: 2391-5455

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topToufik Mansour, and Mark Shattuck. "Restricted partitions and q-Pell numbers." Open Mathematics 9.2 (2011): 346-355. <http://eudml.org/doc/268972>.

@article{ToufikMansour2011,

abstract = {In this paper, we provide new combinatorial interpretations for the Pell numbers p n in terms of finite set partitions. In particular, we identify six classes of partitions of size n, each avoiding a set of three classical patterns of length four, all of which have cardinality given by p n. By restricting the statistic recording the number of inversions to one of these classes, and taking it jointly with the statistic recording the number of blocks, we obtain a new polynomial generalization of p n. Similar considerations using the comajor index statistic yields a further generalization of the q-Pell number studied by Santos and Sills.},

author = {Toufik Mansour, Mark Shattuck},

journal = {Open Mathematics},

keywords = {Pattern avoidance; Inversion; Comajor index; Pell number; q-generalization; pattern avoidance; inversion; comajor index; -generalization},

language = {eng},

number = {2},

pages = {346-355},

title = {Restricted partitions and q-Pell numbers},

url = {http://eudml.org/doc/268972},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Toufik Mansour

AU - Mark Shattuck

TI - Restricted partitions and q-Pell numbers

JO - Open Mathematics

PY - 2011

VL - 9

IS - 2

SP - 346

EP - 355

AB - In this paper, we provide new combinatorial interpretations for the Pell numbers p n in terms of finite set partitions. In particular, we identify six classes of partitions of size n, each avoiding a set of three classical patterns of length four, all of which have cardinality given by p n. By restricting the statistic recording the number of inversions to one of these classes, and taking it jointly with the statistic recording the number of blocks, we obtain a new polynomial generalization of p n. Similar considerations using the comajor index statistic yields a further generalization of the q-Pell number studied by Santos and Sills.

LA - eng

KW - Pattern avoidance; Inversion; Comajor index; Pell number; q-generalization; pattern avoidance; inversion; comajor index; -generalization

UR - http://eudml.org/doc/268972

ER -

## References

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