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Alexandersson, Per
Publications (5 of 5) Show all publications
Alexandersson, P. & Jordan, L. (2019). Enumeration of Border-Strip Decompositions and Weil-Petersson Volumes. Journal of Integer Sequences, 22(4), Article ID 19.4.5.
Open this publication in new window or tab >>Enumeration of Border-Strip Decompositions and Weil-Petersson Volumes
2019 (English)In: Journal of Integer Sequences, ISSN 1530-7638, E-ISSN 1530-7638, Vol. 22, no 4, article id 19.4.5Article in journal (Refereed) Published
Abstract [en]

We describe an injection from border-strip decompositions of certain diagrams to permutations. This allows us to provide enumeration results as well as q-analogues of enumeration formulas. Finally, we use this injection to prove a connection between the number of border-strip decompositions of the n x 2n rectangle and the Weil-Petersson volume of the moduli space of an n-punctured Riemann sphere.

Place, publisher, year, edition, pages
UNIV WATERLOO, 2019
Keywords
border-strip decomposition, permutation, q-analogue, Weil-Petersson volume, rectangular shape
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-255466 (URN)000473287400001 ()
Note

QC 20190918

Available from: 2019-09-18 Created: 2019-09-18 Last updated: 2019-09-18Bibliographically approved
Alexandersson, P. (2019). Polytopes and Large Counterexamples. Experimental Mathematics, 28(1), 115-120
Open this publication in new window or tab >>Polytopes and Large Counterexamples
2019 (English)In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 28, no 1, p. 115-120Article in journal (Refereed) Published
Abstract [en]

In this short note, we give large counterexamples to natural questions about certain order polytopes, in particular, Gelfand–Tsetlin polytopes. Several of the counterexamples are too large to be discovered via a brute-force computer search. We also show that the multiset of hooks in a Young diagram is not enough information to determine the Ehrhart polynomial for an associated order polytope. This is somewhat counter-intuitive to the fact that the multiset of hooks always determine the leading coefficient of the Ehrhart polynomial.

Place, publisher, year, edition, pages
TAYLOR & FRANCIS INC, 2019
Keywords
polytopes, counter-examples, hook formula, Ehrhart polynomial, Kostka coefficient
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-250885 (URN)10.1080/10586458.2017.1361367 (DOI)000464579100010 ()2-s2.0-85030153152 (Scopus ID)
Note

QC 20190507

Available from: 2019-05-07 Created: 2019-05-07 Last updated: 2019-06-11Bibliographically approved
Amini, N. & Alexandersson, P. (2019). The cone of cyclic sieving phenomena. Discrete Mathematics, 342(6), 1581-1601
Open this publication in new window or tab >>The cone of cyclic sieving phenomena
2019 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 342, no 6, p. 1581-1601Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
cyclic sieving, stretched schur polynomial, convex polytope
National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-250764 (URN)10.1016/j.disc.2019.01.037 (DOI)000466833400006 ()2-s2.0-85062678575 (Scopus ID)
Note

QC 20190510

Available from: 2019-05-05 Created: 2019-05-05 Last updated: 2019-05-29Bibliographically approved
Alexandersson, P. & Panova, G. (2018). LLT polynomials, chromatic quasisymmetric functions and graphs with cycles. Discrete Mathematics, 341(12), 3453-3482
Open this publication in new window or tab >>LLT polynomials, chromatic quasisymmetric functions and graphs with cycles
2018 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 341, no 12, p. 3453-3482Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV, 2018
Keywords
Chromatic quasisymmetric functions, Elementary symmetric functions, LLT polynomials, Orientations, Unit interval graphs, Positivity, Diagonal harmonics
National Category
Discrete Mathematics
Identifiers
urn:nbn:se:kth:diva-238893 (URN)10.1016/j.disc.2018.09.001 (DOI)000448496500020 ()2-s2.0-85053911752 (Scopus ID)
Note

QC 20181126

Available from: 2018-11-26 Created: 2018-11-26 Last updated: 2018-11-26Bibliographically approved
Alexandersson, P. & Sawhney, M. (2017). A Major-Index Preserving Map on Fillings. The Electronic Journal of Combinatorics, 24(4), Article ID P4.3.
Open this publication in new window or tab >>A Major-Index Preserving Map on Fillings
2017 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 24, no 4, article id P4.3Article in journal (Refereed) Published
Abstract [en]

We generalize a map by S. Mason regarding two combinatorial models for key polynomials, in a way that accounts for the major index. Furthermore we define a similar variant of this map, that regards alternative models for the modified Macdonald polynomials at t = 0, and thus partially answers a question by J. Haglund. These maps together imply a certain uniqueness property regarding inversion- and coinversion-free fillings. These uniqueness properties allow us to generalize the notion of charge to a non-symmetric setting, thus answering a question by A. Lascoux and the analogous question in the symmetric setting proves a conjecture by K. Nelson.

National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-218233 (URN)000414866100006 ()2-s2.0-85031091360 (Scopus ID)
Note

QC 20171128

Available from: 2017-11-28 Created: 2017-11-28 Last updated: 2017-11-28Bibliographically approved
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