Shareshian wachs

Author: wesc

August undefined, 2024

WebbShareshian and Wachs showed that if G is the incomparability graph of a natural unit interval order then X Gpx,tqis a polynomial with very nice properties. They also made a conjecture on the e-positivity and the e-unimodality of X Gpx,tq. WebbThe Shareshian-Wachs Conjecture In the talk, I will explain the Shareshian-Wachs conjecture and my recent work with Timothy Chow which proves it. The conjecture, …

Chromatic symmetric functions of Dyck paths and q-rook theory

WebbAbstract: In 2015, Brosnan and Chow, and independently Guay-Paquet, proved the Shareshian--Wachs conjecture, which links the combinatorics of chromatic symme... WebbShareshian and Wachs used an involution which is similar to, but not the same as, the involution for e n in their determination of the coefficient ofp n in X(inc(P);x,t). There have been other applications of The Method The height of a poset P, htP, is the number of elements in a longest chain. chint socket

Eulerian quasisymmetric functions - ScienceDirect

WebbWe combine these tools to present two recent applications developed by Shareshian and Wachs. The first application is a quasisymmetric … WebbOur proof uses previous work of Stanley, Gasharov, Shareshian–Wachs, and Brosnan–Chow, as well as results of the second author on the geometry and … WebbAs discussed in the introduction, Shareshian and Wachs conjectured in [16] that the above “dot action” representation on H. ∗ (Hess(S,h)) is related to the well-known Stanley–Stembridge conjecture. Speciﬁcally, they conjectured a tight relationship between the chromatic Hessenberg function of the incomparability granny wheelchair

GEOMETRY OF REGULAR HESSENBERG VARIETIES SpringerLink

The cohomology of abelian Hessenberg varieties and the Stanley ...

WebbRhoades, Serrano, Shareshian, Wachs. Suppose S is a set and let C be a ﬁnite cyclic group acting on S. If g 2C, we let Sg = ft 2S : gt = tg and o(g) = order of g in C. We also let!d = primitive dth root of unity. Finally, suppose we are given f(q) 2R[q], a polynomial in q. WebbGeneralizations of (1.1) appear in the paper [21] of Shareshian and Wachs. For a poset Pwith unique minimum element ^0, P will denote Pnf^0g. For a prime power q>1 and a positive integer n, the poset of all subspaces of an n-dimensional vector space over the q-element eld F q will be denoted by B n(q). Also, D n will denote the set of all granny went to marketWebb4 SHARESHIAN AND WACHS (1) Our conjecture that the generalized q-Eulerian polynomials are unimodal (Conjecture 3.3). This would follow from Theorem 1.1 and the hard Lefschetz theorem applied to Tymoczko’s repre-sentation on the cohomology of the Hessenberg variety. (2) Tymoczko’s problem of nding a decomposition of her repre- granny went to market activities

"Webb21 juni 2011 · John Shareshian, Michelle L. Wachs. We discuss three distinct topics of independent interest; one in enumerative combinatorics, one in symmetric function … " - Shareshian wachs

Shareshian wachs

Chordal and sequentially Cohen-Macaulay clutters

WebbIn 2010 Chung-Graham-Knuth proved an interesting symmetric identity for the Eulerian numbers and asked for a q-analog version. Using the q-Eulerian polynomials introduced by Shareshian-Wachs we find such a q-identity. Moreover, we provide a bijective proof that we further generalize to prove other symmetric qidentities using a combinatorial model due …

Did you know?

WebbMichelle Wachs University of Miami Based on joint work with John Shareshian. Classical Permutation Statistics For σ in symmetric group S n ... Conjecture (Shareshian & MW … WebbShareshian–Wachs q-analogue have important connections to Hessenberg varieties, diagonal harmonics and LLT polynomials. In the case of, so called, abelian Dyck paths …

WebbWe will briefly describe this conjecture, and then explain how recent work of Shareshian-Wachs, Brosnan-Chow, among others, makes a surprising connection between this conjecture and the geometry of Hessenberg varieties, together with a certain symmetric-group representation on the cohomology of Hessenberg varieties. WebbJOHN SHARESHIAN AND MICHELLE L. WACHS (Communicated by Sergei Fomin) Abstract. In this research announcement we present a new q-analog of a classical …

WebbThrough the links connected to the speakers' names you find titles and abstracts of talks as well as links to their homepages. A full program for the meeting is available here and on the AMS program page.. Click here to obtain further information for speakers and participants concerning abstract submission, location of the meeting, travel, and more. WebbWe extend the definition of chordal from graphs to clutters. The resulting family generalizes both chordal graphs and matroids, and obeys many of the same algebraic and geometric properties. Specifically, the independe…

WebbSLIDE POSITIVITY OF CHROMATIC NONSYMMETRIC POLYNOMIALS 3 2.2. Partial Dyck paths and associated graphs. Let n and r be nonnegative integers. We definePn,r to be set of lattice paths that begin at (0,r), end at (n+r,n+r), take unit north and east steps, and stay weakly above the line y = x.We refer to elements of Pn,r as partial Dyck paths. We next …

Webb1 mars 2024 · Examples of this latter approach include the chromatic quasisymmetric function and Shareshian-Wachs conjecture of [SW16] (further studied in [AN21, AS22, CH22, CMP23]), ... chin tsai uninterrupted loveWebb20 dec. 2010 · E-mail addresses: [email protected] (J. Shareshian), [email protected] (M.L. Wachs). 1 Supported in part by NSF Grants DMS 0300483 and DMS 0604233, and the Mittag-Leffler Institute. 2 Supported in part by NSF Grants DMS 0302310 and DMS 0604562, and the Mittag-Leffler Institute. 0001-8708/$ â€“ see front … chint singaporeWebb21 jan. 2016 · Brosnan and Chow's proof is based in part on the idea of deforming the Hessenberg varieties. The proof given here, in contrast, is based on the idea of … granny wheelchair math gamesWebb25 aug. 2024 · Moreover we present a natural generalization of the Shareshian-Wachs conjecture that involves generalized Hessenberg varieties and provide an elementary … granny where is the car keyWebbTraductions en contexte de "Wach fut" en français-anglais avec Reverso Context : Pour marquer son 40e anniversaire, Wach fut officiellement promu royal peintre (1827). granny where are youWebbEulerian quasisymmetric functions were introduced by Shareshian and Wachs in order to obtain a q-analog of Euler's exponential generating function formula for the Eulerian numbers. They are defined via the symmetric group, and applying the stable and nonstable principal specializations yields formulas for joint distributions of permutation statistics. granny white church of christWebb3 mars 2024 · J. Shareshian, M. L. Wachs, Chromatic quasisymmetric functions and Hessenberg varieties, in: Configuration Spaces, CRM Series, Vol. 14, Ed. Norm., Pisa, … granny white handmade cookies