A combinatorial statistic for labeled threshold graphs

Deshpande, Priyavrat; Menon, Krishna; Singh, Anurag K.

doi:10.54550/eca2021v1s3r22

Cited by 1 publication

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“…Statistics. The characteristic polynomial of the threshold arrangement and a statistic on its regions whose distribution is given by the characteristic polynomial has been studied in [9]. This is done by directly looking at the coefficients of the characteristic polynomial.…”

Section: Example 72 We Can Use a Series Of T Moves On A Sketch As Fol...mentioning

confidence: 99%

“…This is done by directly looking at the coefficients of the characteristic polynomial. In fact, even the coefficients of the characteristic polynomial of the Fubini arrangement (Section 7.1.1) have already been combinatorially interpreted in [9,Section 4.1]. This can be used to define an appropriate statistic on the regions of the Fubini arrangement.…”

Section: Example 72 We Can Use a Series Of T Moves On A Sketch As Fol...mentioning

confidence: 99%

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A branch statistic for trees: interpreting coefficients of the characteristic polynomial of braid deformations

Deshpande¹,

Menon²

2022

ECA

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A. The collection of reflecting hyperplanes of a finite Coxeter group is called a reflection arrangement and it appears in many subareas of combinatorics and representation theory. We focus on the problem of counting regions of reflection arrangements and their deformations. Inspired by the recent work of Bernardi, we show that the notion of moves and sketches can be used to provide a uniform and explicit bijection between regions of (the Catalan deformation of ) a reflection arrangement and certain non-nesting partitions. We then use the exponential formula to describe a statistic on these partitions such that distribution is given by the coefficients of the characteristic polynomial. Finally, we consider a sub-arrangement of type C arrangement called the threshold arrangement and its Catalan and Shi deformations.

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Section: Example 72 We Can Use a Series Of T Moves On A Sketch As Fol...mentioning

confidence: 99%

Section: Example 72 We Can Use a Series Of T Moves On A Sketch As Fol...mentioning

confidence: 99%

A branch statistic for trees: interpreting coefficients of the characteristic polynomial of braid deformations

Deshpande¹,

Menon²

2022

ECA

View full text Add to dashboard Cite

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A combinatorial statistic for labeled threshold graphs

Cited by 1 publication

References 0 publications

A branch statistic for trees: interpreting coefficients of the characteristic polynomial of braid deformations

A branch statistic for trees: interpreting coefficients of the characteristic polynomial of braid deformations

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