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Alexandersson, Per

Open this publication in new window or tab >>Enumeration of Border-Strip Decompositions and Weil-Petersson Volumes### Alexandersson, Per

### Jordan, Linus

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()2-s2.0-85073302062 (Scopus ID)
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

Ecole Polytech Fed Lausanne, Dept Math, CH-1015 Lausanne, Switzerland..

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.

QC 20190918

Available from: 2019-09-18 Created: 2019-09-18 Last updated: 2020-02-04Bibliographically approvedOpen this publication in new window or tab >>Polytopes and Large Counterexamples### Alexandersson, Per

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_j_idt371",{id:"formSmash:j_idt184:1:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_j_idt371",multiple:true});
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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20190507

Available from: 2019-05-07 Created: 2019-05-07 Last updated: 2019-06-11Bibliographically approvedOpen this publication in new window or tab >>The cone of cyclic sieving phenomena### Amini, Nima

### Alexandersson, Per

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20190510

Available from: 2019-05-05 Created: 2019-05-05 Last updated: 2019-05-29Bibliographically approvedOpen this publication in new window or tab >>LLT polynomials, chromatic quasisymmetric functions and graphs with cycles### Alexandersson, Per

### Panova, Greta

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_j_idt365",{id:"formSmash:j_idt184:3:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt365",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_j_idt371",{id:"formSmash:j_idt184:3:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt371",multiple:true});
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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20181126

Available from: 2018-11-26 Created: 2018-11-26 Last updated: 2018-11-26Bibliographically approvedOpen this publication in new window or tab >>A Major-Index Preserving Map on Fillings### Alexandersson, Per

### Sawhney, Mehtaab

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 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]

##### National Category

Mathematics
##### Identifiers

urn:nbn:se:kth:diva-218233 (URN)000414866100006 ()2-s2.0-85031091360 (Scopus ID)
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_j_idt365",{id:"formSmash:j_idt184:4:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_j_idt365",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_j_idt371",{id:"formSmash:j_idt184:4:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_j_idt371",multiple:true});
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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20171128

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