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Träfflista för sökning "L773:0012 365X OR L773:1872 681X ;pers:(Alexandersson Per)"

Sökning: L773:0012 365X OR L773:1872 681X > Alexandersson Per

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1.
  • Alexandersson, Per, et al. (författare)
  • LLT polynomials, chromatic quasisymmetric functions and graphs with cycles
  • 2018
  • Ingår i: Discrete Mathematics. - : ELSEVIER SCIENCE BV. - 0012-365X .- 1872-681X. ; 341:12, s. 3453-3482
  • Tidskriftsartikel (refereegranskat)abstract
    • We use a Dyck path model for unit-interval graphs to study the chromatic quasisymmetric functions introduced by Shareshian and Wachs, as well as unicellular LLT polynomials, revealing some parallel structure and phenomena regarding their e-positivity. The Dyck path model is also extended to circular arc digraphs to obtain larger families of polynomials, giving a new extension of LLT polynomials. Carrying over a lot of the noncircular combinatorics, we prove several statements regarding the e-coefficients of chromatic quasisymmetric functions and LLT polynomials, including a natural combinatorial interpretation for the e-coefficients for the line graph and the cycle graph for both families. We believe that certain e-positivity conjectures hold in all these families above. Furthermore, beyond the chromatic analogy, we study vertical-strip LLT polynomials, which are modified Hall-Littlewood polynomials. 
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2.
  • Amini, Nima, et al. (författare)
  • The cone of cyclic sieving phenomena
  • 2019
  • Ingår i: Discrete Mathematics. - : Elsevier. - 0012-365X .- 1872-681X. ; 342:6, s. 1581-1601
  • Tidskriftsartikel (refereegranskat)abstract
    • We study cyclic sieving phenomena (CSP) on combinatorial objects from an abstract point of view by considering a rational polyhedral cone determined by the linear equations that define such phenomena. Each lattice point in the cone corresponds to a non-negative integer matrix which jointly records the statistic and cyclic order distribution associated with the set of objects realizing the CSP. In particular we consider a universal subcone onto which every CSP matrix linearly projects such that the projection realizes a CSP with the same cyclic orbit structure, but via a universal statistic that has even distribution on the orbits.Reiner et.al. showed that every cyclic action gives rise to a unique polynomial (mod q^n-1) complementing the action to a CSP. We give a necessary and sufficient criterion for the converse to hold. This characterization allows one to determine if a combinatorial set with a statistic gives rise (in principle) to a CSP without having a combinatorial realization of the cyclic action. We apply the criterion to conjecture a new CSP involving stretched Schur polynomials and prove our conjecture for certain rectangular tableaux. Finally we study some geometric properties of the CSP cone. We explicitly determine its half-space description and in the prime order case we determine its extreme rays.
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  • Resultat 1-2 av 2
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tidskriftsartikel (2)
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refereegranskat (2)
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Alexandersson, P... (2)Ta bort avgränsningen
Panova, Greta (1)
Amini, Nima (1)
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Kungliga Tekniska Högskolan (2)
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Engelska (2)
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