Distribution of the intertwining number on perfect matchings

Authors

  • Yonah Cherniavsky Department of Mathematics, Ariel University, Ariel, Israel
  • Yuval Khachatryan-Raziel Department of Mathematics, Ariel University, Ariel, Israel

DOI:

https://doi.org/10.3842/umzh.v78i5-6.9374

Keywords:

perfect matchings, intertwining number, Bruhat order, fixed-point-free involutions

Abstract

UDC 519.11, 519.17, 512.54

Ehrenborg and Readdy defined the intertwining number on set partitions. Considering this statistic on perfect matchings, we provide an additional combinatorial description and present an explicit generating function. In particular, we show that the intertwining number on perfect matchings is essentially equidistributed with the rank function of the strong Bruhat order on fixed-point-free involutions of the symmetric group.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 5-6, 2026.

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Published

29.05.2026

Issue

Vol. 78 No. 5-6 (2026)

Section

Research articles